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

TL;DR

This paper develops a continuous anisotropic damage model based on discrete beam-particle simulations to capture crack-induced anisotropy in 2D materials, providing insights into damage evolution and symmetry bounds.

Contribution

It introduces a novel approach combining discrete simulations with harmonic decomposition to model anisotropic damage and estimate symmetry bounds in 2D materials.

Findings

Effective elasticity tensor evolution characterized up to failure

Harmonic decomposition estimates damage-induced anisotropy

Upper bound of distance to orthotropic symmetry class obtained

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. 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. As a by-product of present work we obtain an upper bound of the distance to the orthotropic symmetry class of bi-dimensional elasticity.