Thermomechanical couplings in shape memory alloy materials

In this work we address several theoretical and computational issues which are related to the thermomechanical modeling of shape memory alloy materials. More specifically, in this paper we revisit a non-isothermal version of the theory of large deformation generalized plasticity which is suitable for describing the multiple and complex mechanisms occurring in these materials during phase transformations. We also discuss the computational implementation of a generalized plasticity based constitutive model and we demonstrate the ability of the theory in simulating the basic patterns of the experimentally observed behavior by a set of representative numerical examples

A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model

Loi de comportement et processus stochastique

Le but de ce travail est de présenter un nouveau contexte mathématique qui permette de modéliser d’une façon naturelle le comportement mécanique de la matière. Dans un tel modèle, il est très facile d’effectuer la transition entre la structure microscopique et le comportement macroscopique. Ce point de vue met en oeuvre une théorie mathématique alternative appelée RFS (Radically Frequentist Statistics) basée sur un concept idéalisé d’une très grande séquence finie de résultats

Multi-scale Modelling of Fracture in Open-Cell Metal Foams

Metal foams possess attractive mechanical properties like high stiffness to weight ratio.When used to build light-weight structures they require a good combination of strength and ductility. They are ductile under compression but rather brittle in tension with a few percent of overall strain to fracture. Second-phase particles, grain boundary precipitates and inclusions are often associated with the knock-down of the ductility. Through a heat treatment the microstructure can be changed, however, this also changes the associated yield stress and hardening behaviour of the strut material. How this will affect the overall behaviour depends sensitively on the foam’s cellular architecture, e.g. the cell size and shape distribution, the cross-sectional geometry of the strut, and its relative density. The goal of this work is to study these dependencies using a multi-scale modelling framework that takes all these ingredients into account. In this paper, we present the combined effect of the solid material strain hardening and the relative density on the initiation and accumulation of damage and overall strength of the structure