This review presents the potential that lattice (or spring network) models hold for
micromechanics applications. The models have their origin in the atomistic representations …

In order to found continuum mechanics, two different postulations have been used. The first,
introduced by Lagrange and Piola, starts by postulating how the work expended by internal …

This article, written in honor of Professor Nemat-Nasser, provides an update of the standard
theories of dislocation dynamics, plasticity and elasticity properly modified to include scale …

Various deformation models incorporating higher-order gradients are discussed and their
implications are considered in a variety of problems ranging from the determination of the …

Mechanical behavior of materials with granular microstructures is confounded by unique
features of their grain-scale mechano-morphology, such as the tension–compression …

We study the statics of some trusses, ie networks of nodes linked by linear springs. The
trusses are designed in such a way that a few number of floppy modes are present and …

Abstract Navier–Cauchy format for Continuum Mechanics is based on the concept of contact
interaction between sub-bodies of a given continuous body. In this paper, it is shown how …

Peridynamics is a formulation of continuum mechanics based on integral equations. It is a
nonlocal model, accounting for the effects of long-range forces. Correspondingly, classical …

We present here a limiting process allowing us to write some continuum mechanics models
as a natural asymptotic of molecular models. The approach is based on the hypothesis that …

Previous experiments have shown that stress-induced martensitic transformation in certain
polycrystalline NiTi shape memory alloys can lead to strain localization and propagation …