Continuous anisotropic damage as a twin modelling of discrete bi-dimensional fracture

Abstract

In this contribution, the use of discrete simulations to formulate an anisotropic damage model is investigated. It is proposed to use a beam–particle model to perform numerical characterization tests. Indeed, this discrete model explicitly describes cracking by allowing displacement discontinuities and thus capture crack induced anisotropy of quasi-brittle materials such as concrete. Through 2D discrete simulations, the evolution of the effective elasticity tensor for various loading tests, up to failure, is obtained. The analysis of these tensors through bi-dimensional harmonic decomposition is then performed to estimate the tensorial damage evolution. It is shown in a quantitative manner that a second order –instead of a fourth order– damage tensor is sufficient in practice, even when the micro-cracks are strongly interacting. As a by-product of present work we obtain an upper bound of the distance to the orthotropic symmetry class of bi-dimensional elasticity.