A multifield continuum model for the description of the response of microporous/microcracked composite materials

The description of the mechanical behavior of composite materials is an open challenge in engineering. The focus of this work is on micro-cracked/micro-porous composites, made of stiff grains embedded in a cracked or porous deformable matrix. Grains interact between each other and with cracks or pores localized at the interfaces, which reduce the contact area between grains. Pores’ interaction is also taken into account. We apply a two-scale modeling strategy based on a discrete to scale-dependent (non-classical) continuum equivalence procedure. The constitutive relationships of the resulting microcontinuum, identified by requiring equivalence, in terms of virtual work, between discrete and continuum non-local descriptions of the reference material, take directly into account the material internal structure, and, in particular, material internal lengths. Field and boundary conditions of the equivalent continuum are also derived based on work equivalence between internal and external actions. The response of the obtained one-dimensional equivalent model and of a finite element model of a bar with pores are compared. A good match was obtained in a wide range of pore densities.