Constitutive Relations for Elastic Microcracked Bodies: From a Lattice Model to a Multifield Continuum Description

Abstract

A continuum model suitable for the description of microcracked bodies is shown. The influence of microcracks on the mechanical behavior of the body is estimated through a microstructural field added to the displacement one. This field represents the perturbation to the regular displacement field due to the presence of microcracks. It is an observable quantity; its rate must satisfy appropriate balance equations. The problem of deriving constitutive relations for such a model at least in the linear elastic case is dealt with. Constitutive equations are deduced from a lattice model using an integral identification procedure based on the equivalence in terms of virtual work, without resorting to limit processes. The discrete model considered is made of two superposed lattices; the first one is constituted of material points connected by elastic links; the second one is made of empty closed shells interacting between themselves and with the first lattice. As sample test, a one-dimensional problem is shown.