The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.

UR - http://www.sciencedirect.com/science/article/pii/S0022509619306106 ER - TY - RPRT T1 - Foldable structures made of hydrogel bilayers Y1 - 2018 A1 - Virginia Agostiniani A1 - Antonio DeSimone A1 - Alessandro Lucantonio A1 - Danka Lučić ER - TY - JOUR T1 - Peristaltic Waves as Optimal Gaits in Metameric Bio-Inspired Robots JF - Frontiers in Robotics and AI Y1 - 2018 A1 - Daniele Agostinelli A1 - François Alouges A1 - Antonio DeSimone KW - Biomimetic robots KW - Crawling motility KW - Lumbricus terrestris KW - Metameric robots KW - Optimization KW - Peristalsis KW - Self-propulsion KW - Soft robotics AB -*Peristalsis*, i.e., a motion pattern arising from the propagation of muscle contraction and expansion waves along the body, is a common locomotion strategy for limbless animals. Mimicking peristalsis in bio-inspired robots has attracted considerable attention in the literature. It has recently been observed that maximal velocity in a metameric earthworm-like robot is achieved by actuating the segments using a “phase coordination” principle. This paper shows that, in fact, peristalsis (which requires not only phase coordination, but also that all segments oscillate at same frequency and amplitude) emerges from optimization principles. More precisely, basing our analysis on the assumption of small deformations, we show that peristaltic waves provide the optimal actuation solution in the ideal case of a periodic infinite system, and that this is approximately true, modulo edge effects, for the real, finite length system. Therefore, this paper confirms the effectiveness of mimicking peristalsis in bio-inspired robots, at least in the small-deformation regime. Further research will be required to test the effectiveness of this strategy if large deformations are allowed.

We propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry.

VL - 23 UR - https://doi.org/10.1051/cocv/2017030 ER - TY - JOUR T1 - A natural framework for isogeometric fluid-structure interaction based on BEM-shell coupling JF - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Y1 - 2017 A1 - Luca Heltai A1 - Kiendl, J. A1 - Antonio DeSimone A1 - Alessandro Reali VL - 316 UR - http://cdsads.u-strasbg.fr/abs/2017CMAME.316..522H ER - TY - JOUR T1 - Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler JF - Meccanica Y1 - 2017 A1 - Paolo Gidoni A1 - Antonio DeSimone AB -We formulate and solve the locomotion problem for a bio-inspired crawler consisting of two active elastic segments (i.e., capable of changing their rest lengths), resting on three supports providing directional frictional interactions. The problem consists in finding the motion produced by a given, slow actuation history. By focusing on the tensions in the elastic segments, we show that the evolution laws for the system are entirely analogous to the flow rules of elasto-plasticity. In particular, sliding of the supports and hence motion cannot occur when the tensions are in the interior of certain convex regions (stasis domains), while support sliding (and hence motion) can only take place when the tensions are on the boundary of such regions (slip surfaces). We solve the locomotion problem explicitly in a few interesting examples. In particular, we show that, for a suitable range of the friction parameters, specific choices of the actuation strategy can lead to net displacements also in the direction of higher friction.

VL - 52 UR - https://doi.org/10.1007/s11012-016-0408-0 ER - TY - JOUR T1 - Wet and Dry Transom Stern Treatment for Unsteady and Nonlinear Potential Flow Model for Naval Hydrodynamics Simulations JF - Journal of Ship Research Y1 - 2017 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone AB -We present a model for the fast evaluation of the total drag of ship hulls operating in both wet and dry transom stern conditions, in calm or wavy water, based on the combination of an unsteady semi-Lagrangian potential flow formulation with fully nonlinear free-surface treatment, experimental correlations, and simplified viscous drag modeling. The implementation is entirely based on open source libraries. The spatial discretization is solved using a streamline upwind Petrov‐Galerkin stabilization of an iso-parametric, collocation based, boundary element method, implemented using the open source library deal.II. The resulting nonlinear differential-algebraic system is integrated in time using implicit backward differentiation formulas, implemented in the open source library SUNDIALS. The Open CASCADE library is used to interface the model directly with computer-aided design data structures. The model accounts automatically for hulls with a transom stern, both in wet and dry regimes, by using a specific treatment of the free-surface nodes on the stern edge that automatically detects when the hull advances at low speeds. In this case, the transom stern is partially immersed, and a pressure patch is applied on the water surface detaching from the transom stern, to recover the gravity effect of the recirculating water on the underlying irrotational flow domain. The parameters of the model used to impose the pressure patch are approximated from experimental relations found in the literature. The test cases considered are those of the U.S. Navy Combatant DTMB-5415 and the National Physical Laboratory hull. Comparisons with experimental data on quasi-steady test cases for both water elevation and total hull drag are presented and discussed. The quality of the results obtained on quasi-steady simulations suggests that this model can represent a promising alternative to current unsteady solvers for simulations with Froude numbers below 0.35.

VL - 61 ER - TY - JOUR T1 - Motion planning and motility maps for flagellar microswimmers JF - The European Physical Journal E Y1 - 2016 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone AB -We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

VL - 39 UR - https://doi.org/10.1140/epje/i2016-16072-y ER - TY - CONF T1 - Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model T2 - The 26th International Ocean and Polar Engineering Conference Y1 - 2016 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone A1 - Massimiliano Berti JF - The 26th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers VL - 3 ER - TY - JOUR T1 - Liquid crystal elastomer strips as soft crawlers JF - Journal of the Mechanics and Physics of Solids Y1 - 2015 A1 - Antonio DeSimone A1 - Paolo Gidoni A1 - Giovanni Noselli KW - Crawling motility KW - Directional surfaces KW - Frictional interactions KW - Liquid crystal elastomers KW - Soft biomimetic robots AB -In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, ‘breathing-like’ deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

VL - 84 UR - http://www.sciencedirect.com/science/article/pii/S0022509615300430 ER - TY - JOUR T1 - Motility of a model bristle-bot: A theoretical analysis JF - International Journal of Non-Linear Mechanics Y1 - 2015 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone KW - Bristle-robots KW - Crawling motility KW - Frictional interactions AB -Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

VL - 76 UR - http://www.sciencedirect.com/science/article/pii/S0020746215000025 ER - TY - JOUR T1 - A study of snake-like locomotion through the analysis of a flexible robot model JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2015 A1 - Giancarlo Cicconofri A1 - Antonio DeSimone AB -We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

VL - 471 UR - https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 ER - TY - JOUR T1 - Three-sphere low-Reynolds-number swimmer with a passive elastic arm Y1 - 2015 A1 - Alessandro Montino A1 - Antonio DeSimone AB - One of the simplest model swimmers at low Reynolds number is the three-sphere swimmer by Najafi and Golestanian. It consists of three spheres connected by two rods which change their lengths periodically in non-reciprocal fashion. Here we investigate a variant of this model in which one rod is periodically actuated while the other is replaced by an elastic spring. We show that the competition between the elastic restoring force and the hydrodynamic drag produces a delay in the response of the passive elastic arm with respect to the active one. This leads to non-reciprocal shape changes and self-propulsion. After formulating the equations of motion, we study their solutions qualitatively and numerically. The leading-order term of the solution is computed analytically. We then address questions of optimization with respect to both actuation frequency and swimmer's geometry. Our results can provide valuable conceptual guidance in the engineering of robotic microswimmers. PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34530 U1 - 34735 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Crawling on directional surfaces JF - International Journal of Non-Linear Mechanics Y1 - 2014 A1 - Paolo Gidoni A1 - Giovanni Noselli A1 - Antonio DeSimone KW - Bio-mimetic micro-robots KW - Cell migration KW - Crawling motility KW - Directional surfaces KW - Self-propulsion AB -In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding ‘along the grain’, and high resistance when sliding ‘against the grain’. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

VL - 61 UR - http://www.sciencedirect.com/science/article/pii/S0020746214000213 ER - TY - JOUR T1 - Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost Y1 - 2014 A1 - Giovanni Noselli A1 - Amabile Tatone A1 - Antonio DeSimone KW - Cell migration AB - We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/34449 U1 - 34591 U2 - Mathematics ER - TY - JOUR T1 - An effective model for nematic liquid crystal composites with ferromagnetic inclusions Y1 - 2014 A1 - Maria Carme Calderer A1 - Antonio DeSimone A1 - Dmitry Golovaty A1 - Alexander Panchenko AB - Molecules of a nematic liquid crystal respond to an applied magnetic field by reorienting themselves in the direction of the field. Since the dielectric anisotropy of a nematic is small, it takes relatively large fields to elicit a significant liquid crystal response. The interaction may be enhanced in colloidal suspensions of ferromagnetic particles in a liquid crystalline matrix- ferronematics-as proposed by Brochard and de Gennes in 1970. The ability of these particles to align with the field and simultaneously cause reorientation of the nematic molecules greatly increases the magnetic response of the mixture. Essentially the particles provide an easy axis of magnetization that interacts with the liquid crystal via surface anchoring. We derive an expression for the effective energy of ferronematic in the dilute limit, that is, when the number of particles tends to infinity while their total volume fraction tends to zero. The total energy of the mixture is assumed to be the sum of the bulk elastic liquid crystal contribution, the anchoring energy of the liquid crystal on the surfaces of the particles, and the magnetic energy of interaction between the particles and the applied magnetic field. The homogenized limiting ferronematic energy is obtained rigorously using a variational approach. It generalizes formal expressions previously reported in the physical literature. PB - Society for Industrial and Applied Mathematics Publications UR - http://urania.sissa.it/xmlui/handle/1963/34940 U1 - 35194 U2 - Physics U4 - 1 ER - TY - Generic T1 - A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures T2 - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 Y1 - 2014 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - ship hydrodynamics AB - We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed. JF - Proceedings of the 24th International Ocean and Polar Engineering Conference, Busan, 2014 PB - SISSA U1 - 7357 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D Y1 - 2014 A1 - Luca Heltai A1 - Marino Arroyo A1 - Antonio DeSimone KW - Isogeometric Analysis AB - Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM. PB - Elsevier UR - http://hdl.handle.net/1963/6326 U1 - 6250 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - CONF T1 - Potential Model for Ship Hydrodynamics Simulations Directly Interfaced with CAD Data Structures T2 - The 24th International Ocean and Polar Engineering Conference Y1 - 2014 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone A1 - Massimiliano Berti JF - The 24th International Ocean and Polar Engineering Conference PB - International Society of Offshore and Polar Engineers VL - 4 ER - TY - JOUR T1 - A robotic crawler exploiting directional frictional interactions: experiments, numerics, and derivation of a reduced model JF - Proceedings of the Royal Society A 470, 20140333 (2014) Y1 - 2014 A1 - Giovanni Noselli A1 - Antonio DeSimone AB - We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. ‘breathing-like’ deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations. PB - Royal Society Publishing U1 - 34594 U2 - Mathematics ER - TY - JOUR T1 - Shape control of active surfaces inspired by the movement of euglenids Y1 - 2014 A1 - Marino Arroyo A1 - Antonio DeSimone AB - We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines. PB - Elsevier UR - http://urania.sissa.it/xmlui/handle/1963/35118 U1 - 35375 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Spontaneous division and motility in active nematic droplets Y1 - 2014 A1 - Luca Giomi A1 - Antonio DeSimone AB - We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number. PB - American Physical Society UR - http://urania.sissa.it/xmlui/handle/1963/34902 U1 - 35107 U2 - Mathematics U4 - 1 ER - TY - RPRT T1 - Attainment results for nematic elastomers Y1 - 2013 A1 - Virginia Agostiniani A1 - Gianni Dal Maso A1 - Antonio DeSimone AB - We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids. PB - SISSA UR - http://hdl.handle.net/1963/7174 U1 - 7201 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Crawlers in viscous environments: linear vs nonlinear rheology JF - International Journal of Non-Linear Mechanics 56, 142-147 (2013) Y1 - 2013 A1 - Antonio DeSimone A1 - Federica Guarnieri A1 - Giovanni Noselli A1 - Amabile Tatone AB - We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential forces and slip velocities are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling. PB - Elsevier U1 - 34590 U2 - Mathematics ER - TY - JOUR T1 - Macroscopic contact angle and liquid drops on rough solid surfaces via homogenization and numerical simulations JF - ESAIM: Mathematical Modelling and Numerical Analysis Y1 - 2013 A1 - Cacace, S. A1 - Antonin Chambolle A1 - Antonio DeSimone A1 - Livio Fedeli PB - EDP Sciences VL - 47 ER - TY - JOUR T1 - One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls Y1 - 2013 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -In this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

PB - SISSA UR - http://hdl.handle.net/1963/6467 U1 - 6412 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions JF - Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. Y1 - 2013 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone KW - Unsteady ship-wave interaction AB -We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.

PB - SISSA UR - http://hdl.handle.net/1963/5669 U1 - 5457 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - CHAP T1 - Computing optimal strokes for low reynolds number swimmers T2 - Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, Y1 - 2012 A1 - Antonio DeSimone A1 - Luca Heltai A1 - François Alouges A1 - Lefebvre-Lepot Aline KW - Numerical analysis. AB -We discuss connections between low-Reynolds-number swimming and geometric control theory, and present a general algorithm for the numerical computation of energetically optimal strokes. As an illustration of our approach, we show computed motility maps and optimal strokes for two model swimmers.

JF - Natural locomotion in fluids and on surfaces : swimming, flying, and sliding / editors Stephen Childress, Anette Hosoi, William W. Schultz, and Z. Jane Wang, editors, PB - Springer SN - 9781461439967 UR - http://hdl.handle.net/1963/6445 U1 - 6381 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - JOUR T1 - Crawling motility through the analysis of model locomotors: two case studies JF - The European Physical Journal E, Volume 35, Issue 9, September 2012, Article number85 Y1 - 2012 A1 - Antonio DeSimone A1 - Amabile Tatone AB - We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility. PB - Springer UR - http://hdl.handle.net/1963/7017 U1 - 7014 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Hybridization in nanostructured DNA monolayers probed by AFM: theory versus experiment JF - Nanoscale. 2012 Mar; 4(5):1734-41 Y1 - 2012 A1 - Alessandro Bosco A1 - Fouzia Bano A1 - Pietro Parisse A1 - Loredana Casalis A1 - Antonio DeSimone A1 - Cristian Micheletti AB - Nanografted monolayers (NAMs) of DNA show novel physico-chemical properties that make them ideally suited for advanced biosensing applications. In comparison with alternative solid-phase techniques for diagnostic DNA detection, NAMs have the advantage of combining a small size with a high homogeneity of the DNA surface coverage. These two properties favour the extreme miniaturization and ultrasensitivity in high-throughput biosensing devices. The systematic use of NAMs for quantitative DNA (and protein) detection has so far suffered from the lack of a control on key fabrication parameters, such as the ss- or ds-DNA surface coverage. Here we report on a combined experimental-computational study that allows us to estimate the surface density of the grafted DNA by analyzing the sample mechanical response, that is the DNA patch height vs. applied tip load curves. It is shown that the same analysis scheme can be used to detect the occurrence of hybridization with complementary strands in solution and estimate its efficiency. Thanks to these quantitative relationships it is possible to use a single AFM-based setup to: (i) fabricate a DNA NAM, (ii) control the DNA surface coverage, and (iii) characterize its level of hybridization helping the design of NAMs with pre-determined fabrication parameters. PB - Royal Society of Chemistry U1 - 6998 U2 - Physics U4 - -1 ER - TY - JOUR T1 - Linear elasticity obtained from finite elasticity by Gamma-convergence under weak coerciveness conditions JF - Ann. Inst. H. Poincare Anal. Non Lineaire Y1 - 2012 A1 - Virginia Agostiniani A1 - Gianni Dal Maso A1 - Antonio DeSimone KW - Nonlinear elasticity AB -The energy functional of linear elasticity is obtained as G-limit of suitable rescalings of the energies of finite elasticity...

PB - Gauthier-Villars;Elsevier VL - 29 UR - http://hdl.handle.net/1963/4267 U1 - 3996 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - Generic T1 - Mathematical and numerical modeling of liquid crystal elastomer phase transition and deformation T2 - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 Y1 - 2012 A1 - Mariarita De Luca A1 - Antonio DeSimone KW - Artificial muscle AB - Liquid crystal (in particular, nematic) elastomers consist of cross-linked flexible polymer chains with embedded stiff rod molecules that allow them to behave as a rubber and a liquid crystal. Nematic elastomers are characterized by a phase transition from isotropic to nematic past a temperature threshold. They behave as rubber at high temperature and show nematic behavior below the temperature threshold. Such transition is reversible. While in the nematic phase, the rod molecules are aligned along the direction of the "nematic director". This molecular rearrangement induces a stretch in the polymer chains and hence macroscopic spontaneous deformations. The coupling between nematic order parameter and deformation gives rise to interesting phenomena with a potential for new interesting applications. In the biological field, the ability to considerably change their length makes them very promising as artificial muscles actuators. Their tunable optical properties make them suitable, for example, as lenses for new imaging systems. We present a mathematical model able to describe the behavior of nematic elastomers and numerical simulations reproducing such peculiar behavior. We use a geometrically linear version of the Warner and Terentjev model [1] and consider cooling experiments and stretching experiments in the direction perpendicular to the one of the director at cross-linking. JF - Materials Research Society Symposium Proceedings. Volume 1403, 2012, Pages 125-130 PB - Cambridge University Press SN - 9781605113807 UR - http://hdl.handle.net/1963/7020 U1 - 7011 U2 - Physics U4 - 1 ER - TY - JOUR T1 - Ogden-type energies for nematic elastomers JF - International Journal of Non-Linear mechanics Y1 - 2012 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Nonlinear elasticity AB -Ogden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

PB - Elsevier VL - 47 IS - 2 U1 - 6971 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution JF - Calculus of variations and partial differential equations 44 (2012) 495-541 Y1 - 2012 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Francesco Solombrino AB -Cam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

PB - Springer UR - http://hdl.handle.net/1963/3900 U1 - 809 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Reverse engineering the euglenoid movement JF - Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879 Y1 - 2012 A1 - Marino Arroyo A1 - Luca Heltai A1 - Daniel Millán A1 - Antonio DeSimone KW - microswimmers AB - Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics. UR - http://hdl.handle.net/1963/6444 U1 - 6380 U2 - Mathematics U4 - 1 U5 - MAT/08 ANALISI NUMERICA ER - TY - CONF T1 - A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves T2 - 17th Int. Conf. Ships Shipp. Res. Y1 - 2012 A1 - Andrea Mola A1 - Luca Heltai A1 - Antonio DeSimone JF - 17th Int. Conf. Ships Shipp. Res. ER - TY - JOUR T1 - Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions JF - PNAS 108 (2011) 13978 Y1 - 2011 A1 - Luca Cardamone A1 - Alessandro Laio A1 - Rajesh Shahapure A1 - Antonio DeSimone PB - National Academy of Sciences UR - http://hdl.handle.net/1963/4358 U1 - 4066 U2 - Physics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers JF - SIAM J. Math. Anal. Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -We present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

PB - Society for Industrial and Applied Mathematics VL - 43 UR - http://hdl.handle.net/1963/3894 U1 - 815 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Gamma-convergence of energies for nematic elastomers in the small strain limit JF - Continuum. Mech. Therm. Y1 - 2011 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Liquid crystals AB -We study two variational models recently proposed in the literature to describe the mechanical behaviour of nematic elastomers either in the fully nonlinear regime or in the framework of a geometrically linear theory. We show that, in the small strain limit, the energy functional of the first one I\\\"-converges to the relaxation of the second one, a functional for which an explicit representation formula is available.

PB - Springer VL - 23 UR - http://hdl.handle.net/1963/4141 U1 - 3882 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Metastable equilibria of capillary drops on solid surfaces: a phase field approach JF - Continuum Mechanics and Thermodynamics Y1 - 2011 A1 - Livio Fedeli A1 - Turco, Alessandro A1 - Antonio DeSimone AB -We discuss a phase field model for the numerical simulation of metastable equilibria of capillary drops resting on rough solid surfaces and for the description of contact angle hysteresis phenomena in wetting. The model is able to reproduce observed transitions of drops on micropillars from Cassie–Baxter to Wenzel states. When supplemented with a dissipation potential which describes energy losses due to frictional forces resisting the motion of the contact line, the model can describe metastable states such as drops in equilibrium on vertical glass plates. The reliability of the model is assessed by a detailed comparison of its predictions with experimental data on the maximal size of water drops that can stick on vertical glass plates which have undergone different surface treatments.

VL - 23 UR - https://doi.org/10.1007/s00161-011-0189-6 ER - TY - JOUR T1 - Numerical Strategies for Stroke Optimization of Axisymmetric Microswimmers JF - Mathematical Models and Methods in Applied Sciences 21 (2011) 361-387 Y1 - 2011 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai KW - Optimal swimming AB - We propose a computational method to solve optimal swimming problems, based on the boundary integral formulation of the hydrodynamic interaction between swimmer and surrounding fluid and direct constrained minimization of the energy consumed by the swimmer. We apply our method to axisymmetric model examples. We consider a classical model swimmer (the three-sphere swimmer of Golestanian et al.) as well as a novel axisymmetric swimmer inspired by the observation of biological micro-organisms. PB - World Scientific UR - http://hdl.handle.net/1963/3657 U1 - 648 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications JF - Journal of the Mechanics and Physics of Solids 59 (2011) 787-803 Y1 - 2011 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. UR - http://hdl.handle.net/1963/4065 U1 - 337 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling JF - Calculus of Variations and Partial Differential Equations 40 (2011) 125-181 Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Francesco Solombrino KW - Cam-Clay plasticity AB -Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.

PB - Springer UR - http://hdl.handle.net/1963/3670 U1 - 635 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution of sessile drops and contact angle hysteresis JF - Arch. Rational Mech. Anal. 202 (2011) 295-348 Y1 - 2011 A1 - Giovanni Alberti A1 - Antonio DeSimone AB - We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations. PB - Springer UR - http://hdl.handle.net/1963/4912 U1 - 4693 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - RPRT T1 - Optimally swimming Stokesian Robots Y1 - 2010 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai A1 - Aline Lefebvre A1 - Benoit Merlet AB - We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail. UR - http://hdl.handle.net/1963/3929 U1 - 472 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CONF T1 - A Phase Field Approach to Wetting and Contact Angle Hysteresis Phenomena T2 - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials Y1 - 2010 A1 - Antonio DeSimone A1 - Livio Fedeli A1 - Turco, Alessandro ED - Hackl, Klaus AB -We discuss a phase field model for the numerical simulation of contact angle hysteresis phenomena in wetting. The performance of the model is assessed by comparing its predictions with experimental data on the critical size of drops that can stick on a vertical glass plate.

JF - IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials PB - Springer Netherlands CY - Dordrecht SN - 978-90-481-9195-6 ER - TY - RPRT T1 - The role of membrane viscosity in the dynamics of fluid membranes Y1 - 2010 A1 - Marino Arroyo A1 - Antonio DeSimone A1 - Luca Heltai AB - Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3. UR - http://hdl.handle.net/1963/3930 U1 - 471 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Biological Fluid Dynamics, Non-linear Partial Differential Equations T2 - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 Y1 - 2009 A1 - Antonio DeSimone A1 - François Alouges A1 - Aline Lefebvre JF - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 UR - http://hdl.handle.net/1963/2630 U1 - 1493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers JF - Netw. Heterog. Media 4 (2009) 667-708 Y1 - 2009 A1 - Marco Cicalese A1 - Antonio DeSimone A1 - Caterina Ida Zeppieri AB - In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three continuum models consistent with those commonly employed in the current literature. We also derive the correspondent macroscopic energies in the presence of displacement boundary conditions and of various kinds of applied external fields. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/3788 U1 - 538 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions JF - Math. Models Methods Appl. Sci. 19 (2009) 1643-1711 Y1 - 2009 A1 - Gianni Dal Maso A1 - Antonio DeSimone AB - We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation. UR - http://hdl.handle.net/1963/3395 U1 - 937 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Relaxation dynamics of fluid membranes JF - Phys. Rev. E 79 (2009) 031915 Y1 - 2009 A1 - Marino Arroyo A1 - Antonio DeSimone AB - We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest. PB - American Physical Society UR - http://hdl.handle.net/1963/3618 U1 - 686 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Strain-order coupling in nematic elastomers: equilibrium configurations JF - Math. Models Methods Appl. Sci. 19 (2009) 601-630 Y1 - 2009 A1 - Pierluigi Cesana A1 - Antonio DeSimone AB - We consider models that describe liquid crystal elastomers either in a biaxial or in a uniaxial phase and in the framework of Frank\\\'s director theory. We prove existence of static equilibrium solutions in the presence of frustrations due to electro-mechanical boundary conditions and to applied loads and fields. We find explicit solutions arising in connection with special boundary conditions and the corresponding phase diagrams, leading to significant implications on possible experimental observations. UR - http://hdl.handle.net/1963/2700 U1 - 1400 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Stratos: a code for 3D free surface flows with floating constraints Y1 - 2009 A1 - Antonio DeSimone A1 - B. Bianchi A1 - Luca Heltai AB - This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation\\nof hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a\\nfloating object via Lagrange multipliers...... UR - http://hdl.handle.net/1963/3701 U1 - 604 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II Y1 - 2009 A1 - Antonio DeSimone A1 - Luca Heltai A1 - Cataldo Manigrasso AB - The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly\\nvia the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or\\nthree spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations. UR - http://hdl.handle.net/1963/3700 U1 - 605 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Globally stable quasistatic evolution in plasticity with softening JF - Netw. Heterog. Media 3 (2008) 567-614 Y1 - 2008 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response. UR - http://hdl.handle.net/1963/1965 U1 - 2228 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal Strokes for Low Reynolds Number Swimmers: An Example JF - J. Nonlinear Sci. 18 (2008) 277-302 Y1 - 2008 A1 - François Alouges A1 - Antonio DeSimone A1 - Aline Lefebvre AB - Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics). PB - Springer UR - http://hdl.handle.net/1963/4006 U1 - 396 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Relaxation of some transversally isotropic energies and applications to smectic A elastomers JF - Math. Models Methods Appl. Sci. 18 (2008) 1-20 Y1 - 2008 A1 - James Adams A1 - Sergio Conti A1 - Antonio DeSimone A1 - Georg Dolzmann UR - http://hdl.handle.net/1963/1912 U1 - 2325 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - A vanishing viscosity approach to quasistatic evolution in plasticity with softening JF - Arch. Ration. Mech. Anal. 189 (2008) 469-544 Y1 - 2008 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples. UR - http://hdl.handle.net/1963/1844 U1 - 2373 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Critical voltages and blocking stresses in nematic gels JF - Eur. Phys. J. E 24 (2007) 303-310 Y1 - 2007 A1 - Antonio DeSimone A1 - Antonio Di Carlo A1 - Luciano Teresi AB - We use a recently proposed model to study the dynamics of director remodeling in nematic gels under combined electro-mechanical loading. Focusing on a model specimen, we describe the critical volt-ages that must be exceeded to achieve mesogen reorientation, and the blocking stresses that prevent alignment of the nematic mesogens with the electric field. The corresponding phase diagram shows that the dynamic thresholds defined above are different from those predicted on the sole basis of energetics. Multistep loading programs are used to explore the energy landscape of our model specimen, showing the existence of multiple local minima under the same voltage and applied stress. This leads us to conclude that hysteresis should be expected in the electro-mechanical response of nematic gels. UR - http://hdl.handle.net/1963/2553 U1 - 1566 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - A new model for contact angle hysteresis Y1 - 2007 A1 - Antonio DeSimone A1 - Natalie Gruenewald A1 - Felix Otto AB - We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence. JF - Netw. Heterog. Media 2 (2007) 211-225 UR - http://hdl.handle.net/1963/1848 U1 - 2369 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for pressure-sensitive plastic materials JF - Milan J. Math. 75 (2007) 117-134 Y1 - 2007 A1 - Gianni Dal Maso A1 - Alexey Demyanov A1 - Antonio DeSimone AB - We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity. UR - http://hdl.handle.net/1963/1962 U1 - 2231 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Soft elasticity and microstructure in smectic C elastomers Y1 - 2007 A1 - Antonio DeSimone A1 - James Adams A1 - Sergio Conti AB - Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable. JF - Contin. Mech. Thermodyn. 18 (2007) 319-334 UR - http://hdl.handle.net/1963/1811 U1 - 2403 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Time-dependent systems of generalized Young measures Y1 - 2007 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora A1 - Massimiliano Morini AB - In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time. JF - Netw. Heterog. Media 2 (2007) 1-36 UR - http://hdl.handle.net/1963/1795 U1 - 2749 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - 2-d stability of the Néel wall JF - Calc. Var. Partial Differential Equations 27 (2006) 233-253 Y1 - 2006 A1 - Antonio DeSimone A1 - Hans Knuepfer A1 - Felix Otto AB - We are interested in thin-film samples in micromagnetism, where the magnetization m is a 2-d unit-length vector field. More precisely we are interested in transition layers which connect two opposite magnetizations, so called Néel walls. UR - http://hdl.handle.net/1963/2194 U1 - 2050 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Quasistatic evolution problems for linearly elastic-perfectly plastic materials JF - Arch. Ration. Mech. Anal. 180 (2006) 237-291 Y1 - 2006 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Maria Giovanna Mora AB - The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain. UR - http://hdl.handle.net/1963/2129 U1 - 2114 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Recent analytical developments in micromagnetics T2 - The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. Y1 - 2006 A1 - Antonio DeSimone A1 - Robert V. Kohn A1 - Stefan Müller A1 - Felix Otto JF - The science of hysteresis / eds. Giorgio Bertotti, Isaak D. Mayergoyz. - Amsterdam: Elsevier, 2006. Vol.2, 269-381. SN - 978-0-12-480874-4 UR - http://hdl.handle.net/1963/2230 U1 - 2014 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Self-similar folding patterns and energy scaling in compressed elastic sheets JF - Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 Y1 - 2005 A1 - Sergio Conti A1 - Antonio DeSimone A1 - Stefan Müller AB - Thin elastic sheets under isotropic compression, such as for example blisters formed by thin films which debonded from the substrate, can exhibit remarkably complex folding patterns. We discuss the scaling of the elastic energy with respect to the film thickness, and show that in certain regimes the optimal energy scaling can be reached\\nby self-similar folding patterns that refine towards the boundary, in agreement with experimental observations. We then extend the analysis\\nto anisotropic compression, and discuss a simplified scalar model which suggests the presence of a transition between a regime where\\nthe deformation is governed by global properties of the domain and another one where the direction of maximal compression dominates and the scale of the folds is mainly determined by the distance to the boundary in the direction of the folds themselves. PB - Elsevier UR - http://hdl.handle.net/1963/3000 U1 - 1333 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains JF - Int. J. Numer. Anal. Met. 29 (2005) 73-101 Y1 - 2005 A1 - Antonio DeSimone A1 - Claudio Tamagnini AB - Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.\\nIn this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws. UR - http://hdl.handle.net/1963/2165 U1 - 2079 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Wetting of rough surfaces: a homogenization approach JF - Proc. R. Soc. Lon. Ser. A 461 (2005) 79-97 Y1 - 2005 A1 - Antonio DeSimone A1 - Giovanni Alberti AB - The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact angle is associated with the solution of two cell problems, giving the minimal energy per unit macroscopic area for a transition layer between the rough solid surface and a liquid or vapor phase. Our results are valid for both chemically heterogeneous and homogeneous surfaces. In the latter case, a very transparent structure emerges from the variational\\napproach: the classical laws of Wenzel and Cassie-Baxter give bounds for the optimal energy, and configurations of minimal energy are those leading to the smallest macroscopic contact angle in the hydrophobic case, to the largest one in the hydrophilic case. UR - http://hdl.handle.net/1963/2253 U1 - 1994 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Coarse-grained models of materials with non-convex free-energy: two case studies JF - Computer methods in applied mechanics and engineering , 193 (2004) 5129-5141 Y1 - 2004 A1 - Antonio DeSimone AB - Bridging across length scales is one of the fundamental challenges in the computational modelling of material systems whose mechanical response is driven by rough energy landscapes. The typical feature of such systems is that of exhibiting fine scale microstructures. Two case studies, namely, nematic elastomers and ferromagnetic shape memory alloys, are presented to illustrate the use of modern techniques from (non-convex) calculus of variations in developing coarse-grained models of microstructure-driven material response. PB - Elsevier UR - http://hdl.handle.net/1963/4884 U1 - 4664 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Energetics and switching of quasi-uniform states in small ferromagnetic particles JF - M2AN Math. Model. Numer. Anal. 38 (2004) 235-248 Y1 - 2004 A1 - François Alouges A1 - Sergio Conti A1 - Antonio DeSimone A1 - Ivo Pokern AB - We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size. PB - EDP Sciences UR - http://hdl.handle.net/1963/2999 U1 - 1334 U2 - Mathematics U3 - Functional Analysis and Applications ER -