Macroscale modelling of microstructure damage evolution by a rigid body and spring model

A mechanistic approach is presented for macroscale modelling of a structured solid material. The model consists of an assemblage of rigid mass-elements connected to each other by normal and shear line-springs at each side. The characteristics of these springs govern the macroscopic behaviour of the model that is able to incorporate an internal length and a polarity, in analogy with an orthotropic Cosserat solid material. The present numerical implementation addresses the in-plane modelling of a masonry-like composite whose main macroscopic constitutive aspects are: very low tensile strength, texture-dependent evolution of the damage, and orthotropy of shear strength and internal friction. The constitutive rules are assigned by following a heuristic approach, based on the main in-plane damage mechanisms that are identified at the mesoscale, on a representative volume element of the composite solid material. In particular, specific separate constitutive laws for the normal and the shear springs are adopted. Two numerical tests compare the present macroscale approach with a detailed finite element micromodelling, and demonstrate the capability of the proposed model to describe the main microstructure features of the damaging process with very few degrees of freedom.