As liquids approach the glass transition temperature, dynamical heterogeneity emerges as a crucial universal feature of their behavior. Dynamic facilitation, where local motion triggers further nearby, plays major role in this phenomenon. Here we show that long-range, elastically-mediated facilitation appears below mode-coupling adding to short-range component present at all temperatures. Our r...

The spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE’s in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic c...

The quasi-static evolution of an elastoplastic body with a multi-surface constitutive law of linear kinematic hardening type allows the modeling of curved stress-strain relations. It generalises classical small-strain elastoplasticity from one to various plastic phases. Firstly, we briefly recall a mathematical model represented by an initial-boundary value problem in the form a variational ine...

This paper is devoted to the homogenization for a class of rate-independent systems described by the energetic formulation. The associated nonlinear partial differential system has periodically oscillating coefficients, but has the form of a standard evolutionary variational inequality. Thus, the model applies to standard linearized elastoplasticity with hardening. Using the recently developed ...

The rigorous derivation of lower dimensional models for thin structures is a question of great interest in mechanics and its applications. In the early 90’s a rigorous approach to dimension reduction has emerged in the stationary framework and in the context of nonlinear elasticity. This approach is based on Γ-convergence and, starting from the seminal paper [3, 4], has led to establish a hiera...

Motivated by relaxation in the calculus of variations, this paper addresses convex but not necessarily strictly convex minimization problems. A class of energy functionals is described for which any stress field σ in L(Ω) with div σ in W 1,p ′ (Ω) (from Euler Lagrange equations and smooth lower order terms) belongs to W 1,q loc (Ω). Applications include the scalar double-well potential, an opti...

This paper summarises the general strategy for time evolving finite elastoplasticity and outlines encountered computational challenges in form of numerical benchmarks. Each time-step of some natural implicit time-discretisation is eventually recast into a possibly non-convex minimisation problem. Finite plasticity seems to imply the lack of lower semicontinuity of the energy functional and so l...

We explain an interface for the implementation of rate-independent elastoplasticity which separates the pointwise evaluation of the elastoplastic material law and the global solution of the momentum balance equation. The elastoplastic problem is discretized in time by the implicit Euler method and every time step is solved with a Newton iteration. For the discretization in space the material pa...

An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. Existence and uniqueness of the plastic multiplier is rigorously proved, which allows for the re-formulation of the forward system using a complementarity condition. I...