Related papers: A variational principle for hardening elastoplasti…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
An improved linear model is developed for elasto-plastic and adhesive contact. New correlations are proposed and validated to estimate the key input parameters of the model, including contact stiffness, yield point, maximum pull-off force…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
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…
This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…
The aim of the paper is to propose a paradigm shift for the variational approach of brittle fracture. Both dynamics and the limit case of statics are treated in a same framework. By contrast with the usual incremental approach, we use a…
In this paper, a reliable a posteriori error estimator for a model problem of elastoplasticity with linear kinematic hardening is derived, which satisfies some (local) efficiency estimates. It is applicable to any discretization that is…
Commonly used linear and nonlinear constitutive material models in deformation simulation contain many simplifications and only cover a tiny part of possible material behavior. In this work we propose a framework for learning customized…
A variational discrete element method is applied to simulate quasi-static crack propagation. Cracks are considered to propagate between the mesh cells through the mesh facets. The elastic behaviour is parametrized by the continuous…
The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
The plasticity of amorphous solids undergoing shear is characterized by quasi-localized rearrangements of particles. While many models of plasticity exist, the precise relationship between plastic dynamics and the structure of a particle's…
In this paper we study the vanishing inertia and viscosity limit of a second order system set in an Euclidean space, driven by a possibly nonconvex time-dependent potential satisfying very general assumptions. By means of a variational…
The aim of this review is to highlight the connection between well-established physical and mathematical principles as they pertain to the theory of linear viscoelasticity. We begin by examining the physical foundations of Boltzmann and…
A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the…
We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…
For solving the longstanding materials science problem of correlating elastic properties of a solid material to the formation of cracks we present a new general concept. This concept is applied to the technologically most important cracks…
For monodomain nematic elastomers, we construct generalised elastic-nematic constitutive models combining purely elastic and neoclassical-type strain-energy densities. Inspired by recent developments in stochastic elasticity, we extend…
An elasto-plastic model for concrete, based on a recently-proposed yield surface and simple hardening laws, is formulated, implemented, numerically tested and validated against available test results. The yield surface is smooth and…