Related papers: A note on the derivation of rigid-plastic models

Qualitative properties of a second order elliptic equation from the anisotropic elasticity are investigated. Some explicit solutions for a disk are presented. Behaviour of these solutions in dependence of coefficients is investigated. The…

We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In…

We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain…

A number of current theories of plasticity in amorphous solids assume at their basis that plastic deformations are spatially localized. We present in this paper a series of numerical experiments to test the degree of locality of plastic…

I report on a systematic derivation of the phenomenological ``adhesion approximation'' from gravitational instability together with a brief evaluation of the related status of analytical modeling of large-scale structure.

The response of amorphous materials to an applied strain can be continuous, or instead display a macroscopic stress drop when a shear band nucleates. Such discontinuous response can be observed if the initial configuration is very stable.…

A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered…

We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti, M\"uller, Ortiz, Arch.\ Ration.\ Mech.\ Anal.\ 229, 79-123, 2018. The main focus of this paper concerns the formulation of a…

In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of…

We consider a dynamical elasto-plasticity system with Kelvin--Voigt viscosity and linear kinematic hardening of Melan--Prager type. The model is formulated in a variational framework in which a constraint set for the stress evolves in time…

We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…

In this paper, we investigate some micromechanical aspects of elasto-plasticity in heterogeneous geomaterials. The aim is to upscale the elasto-plastic behavior for a representative volume of the material which is indeed a very challenging…

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its…

Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…

We consider a cylindrical film of fluid adhering to a rigid cylinder of fixed radius. The main result is to give the critical (maximum) length for which such a film of given thickness can be stable. The problem is considered both when the…

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work…

A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which…

A new approach to relativistic elasticity theory is proposed. In this approach the theory becomes a gauge--type theory, with the diffeomorphisms of the material space playing the role of gauge transformations. The dynamics of the elastic…

This work proposes a model for granular deformation that predicts the stress and velocity profiles in well-developed dense granular flows. Recent models for granular elasticity (Jiang and Liu 2003) and rate-sensitive plastic flow (Jop et…

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…