Non-local damage mechanics with evolving interactions for modeling quasi-brittle materials : anisotropic damage and gradient-enhanced Eikonal approach

Predicting the cracking nucleation and propagation is essential to describe structural response under complex loading conditions. Diffuse micro-cracks are observed to appear before coalescing into a macro-crack. In the case of quasi-brittle materials, strain-softening behavior is observed and is related to a progressive loss of stiffness. From a thermodynamics viewpoint, this can be described in a continuum way by a damage state variable.However, local continuum damage mechanics models inevitably lead to an ill-posed rate equilibrium problem. In a finite element context, numerical results are, therefore, mesh-dependent. Non-local damage models can recover mesh-independent results by introducing neighborhood interactions through an internal length. Classic non-local approaches consider isotropic and constant interactions, which cannot reproduce the entire degradation process appropriately. Evolving interaction approaches exist and may better describe the cracking behavior. This thesis aims to provide theoretical and numerical aspects for developing evolving interactions gradient-enhanced damage models. Firstly, non-local models are studied and compared by analyzing boundary effects and damage diffusion in a one-dimensional explicit dynamics spalling test.The Eikonal non-local approach is given attention, where evolving interactions are considered through a damage-dependent Riemannian metric. The gradient-enhanced version of this model (ENLG) is then derived from a differential geometry-based micromorphic framework, leading to a dissipation expression fulfilling thermodynamics second principle. A simplified variational formulation is developed to evaluate the model's capabilities in two-dimensional isotropic damage quasi-static numerical simulations. Finally, the ENLG regularization is coupled to an anisotropic damage model considering a second-order damage tensor. Damage-induced anisotropy is naturally considered in the behavior and the evolving interactions. Simulations in two and three-dimensional contexts are studied and compared to existing experimental results from the literature while highlighting the numerical aspects involved. A detailed analysis describes the advantages of considering anisotropic damage and damage-dependent anisotropic interactions.