TY - RPRT
T1 - On the effect of interactions beyond nearest neighbours on non-convex lattice systems
Y1 - 2017
A1 - Roberto Alicandro
A1 - Giuliano Lazzaroni
A1 - Mariapia Palombaro
AB - We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation.
UR - http://urania.sissa.it/xmlui/handle/1963/35268
U1 - 35574
U2 - Mathematics
U4 - 1
ER -
TY - JOUR
T1 - Existence and uniqueness of dynamic evolutions for a peeling test in dimension one
JF - Journal of Differential Equations
Y1 - 2016
A1 - Gianni Dal Maso
A1 - Giuliano Lazzaroni
A1 - Lorenzo Nardini
KW - Dynamic debonding
KW - Dynamic energy release rate
KW - Dynamic fracture
KW - Griffith's criterion
KW - Maximum dissipation principle
KW - Wave equation in time-dependent domains
AB - In this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

VL - 261
UR - http://www.sciencedirect.com/science/article/pii/S0022039616301772
ER -
TY - JOUR
T1 - Energy release rate and stress intensity factor in antiplane elasticity
JF - Journal de Mathematiques Pures et Appliquees 95 (2011) 565-584
Y1 - 2011
A1 - Giuliano Lazzaroni
A1 - Rodica Toader
AB - In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C1,1 curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks.
PB - Elsevier
UR - http://hdl.handle.net/1963/3780
U1 - 546
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -