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.

%B Meccanica %V 52 %P 587–601 %8 Feb %G eng %U https://doi.org/10.1007/s11012-016-0408-0 %R 10.1007/s11012-016-0408-0 %0 Conference Paper %B The 26th International Ocean and Polar Engineering Conference %D 2016 %T Ship Sinkage and Trim Predictions Based on a CAD Interfaced Fully Nonlinear Potential Model %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %A Massimiliano Berti %B The 26th International Ocean and Polar Engineering Conference %I International Society of Offshore and Polar Engineers %V 3 %P 511–518 %G eng %0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2015 %T A study of snake-like locomotion through the analysis of a flexible robot model %A Giancarlo Cicconofri %A Antonio DeSimone %XWe 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.

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 471 %P 20150054 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2015.0054 %R 10.1098/rspa.2015.0054 %0 Journal Article %D 2014 %T Shape control of active surfaces inspired by the movement of euglenids %A Marino Arroyo %A Antonio DeSimone %X 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. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35118 %1 35375 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T09:19:38Z (GMT) No. of bitstreams: 0 %R 10.1016/j.jmps.2013.09.017 %0 Journal Article %D 2014 %T Spontaneous division and motility in active nematic droplets %A Luca Giomi %A Antonio DeSimone %X 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. %I American Physical Society %G en %U http://urania.sissa.it/xmlui/handle/1963/34902 %1 35107 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-03T14:40:44Z No. of bitstreams: 1 preprint2014.pdf: 4005398 bytes, checksum: eebaadedd03c1077a9cb2a209b5abdcc (MD5) %R 10.1103/PhysRevLett.112.147802 %0 Journal Article %J Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %D 2013 %T A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %K Unsteady ship-wave interaction %XWe 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.

%B Engineering Analysis with Boundary Elements, 37(1):128 – 143, 2013. %I SISSA %G en %U http://hdl.handle.net/1963/5669 %1 5457 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2012-03-16T11:19:51Z\\nNo. of bitstreams: 1\\nMolaHeltaiDeSimone-2012-aa.pdf: 1981527 bytes, checksum: 8a82da009242da0cf884e2c7f04009a6 (MD5) %0 Conference Paper %B 17th Int. Conf. Ships Shipp. Res. %D 2012 %T A stable semi-lagrangian potential method for the simulation of ship interaction with unsteady and nonlinear waves %A Andrea Mola %A Luca Heltai %A Antonio DeSimone %B 17th Int. Conf. Ships Shipp. Res. %G eng %0 Journal Article %J Math. Models Methods Appl. Sci. 19 (2009) 601-630 %D 2009 %T Strain-order coupling in nematic elastomers: equilibrium configurations %A Pierluigi Cesana %A Antonio DeSimone %X 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. %B Math. Models Methods Appl. Sci. 19 (2009) 601-630 %G en_US %U http://hdl.handle.net/1963/2700 %1 1400 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-07-25T15:04:59Z\\nNo. of bitstreams: 1\\nprprCdS.pdf: 504721 bytes, checksum: 2ef9aff006dbc9353a50a122cb98d381 (MD5) %0 Report %D 2009 %T Stratos: a code for 3D free surface flows with floating constraints %A Antonio DeSimone %A B. Bianchi %A Luca Heltai %X 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...... %G en_US %U http://hdl.handle.net/1963/3701 %1 604 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-07-30T14:37:01Z\\nNo. of bitstreams: 1\\nBianchiDeSimoneHeltai.pdf: 899803 bytes, checksum: aff44eb1a39c6fd4acd4b3cb285e2d64 (MD5) %0 Report %D 2007 %T Soft elasticity and microstructure in smectic C elastomers %A Antonio DeSimone %A James Adams %A Sergio Conti %X 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. %B Contin. Mech. Thermodyn. 18 (2007) 319-334 %G en_US %U http://hdl.handle.net/1963/1811 %1 2403 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-04-12T09:42:24Z\\nNo. of bitstreams: 1\\nsissa05M-06.pdf: 394760 bytes, checksum: 95c4183d6cb1210bf2a689ae083a3cb7 (MD5) %R 10.1007/s00161-006-0031-8 %0 Journal Article %J Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %D 2005 %T Self-similar folding patterns and energy scaling in compressed elastic sheets %A Sergio Conti %A Antonio DeSimone %A Stefan Müller %X 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. %B Comput. Methods Appl. Mech. Engrg. 194 (2005) 2534-2549 %I Elsevier %G en_US %U http://hdl.handle.net/1963/3000 %1 1333 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-01T10:37:14Z\\nNo. of bitstreams: 1\\npreprint2004_3.pdf: 907333 bytes, checksum: 2b22c209b91ba2ddacc1a1c14a9054a2 (MD5) %R 10.1016/j.cma.2004.07.044 %0 Journal Article %J Int. J. Numer. Anal. Met. 29 (2005) 73-101 %D 2005 %T Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains %A Antonio DeSimone %A Claudio Tamagnini %X 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. %B Int. J. Numer. Anal. Met. 29 (2005) 73-101 %G en_US %U http://hdl.handle.net/1963/2165 %1 2079 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-10-02T12:02:04Z\\nNo. of bitstreams: 1\\nDeSimoneTamagnini_2005.pdf: 1179767 bytes, checksum: 23b892b2314ea8e2199cc2b2449386b0 (MD5) %R 10.1002/nag.405