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.

在此贡献中，研究了使用离散模拟来制定各向异性损伤模型的方法。建议使用束粒子模型进行数值表征测试。实际上，该离散模型通过允许位移不连续性来明确描述裂纹，从而捕获了准脆性材料（如混凝土）的裂纹诱导各向异性。通过2D离散仿真，获得了有效的弹性张量在各种载荷测试下直至失效的演变过程。然后通过二维谐波分解对这些张量进行分析，以估计张量破坏的演变。定量显示，实际上，即使微裂纹强烈相互作用，二级（而不是四级）损伤张量也足够了。