Fully automatic multigrid adaptive mesh refinement strategy with controlled accuracy for nonlinear quasi-static problems

We propose an adaptive mesh refinement (AMR) algorithm dedicated to the simulation of nonlinear quasi-static solid mechanics problems with complex local phenomena at the structural scale. The proposed method allows us to follow in time the evolution of studied phenomena in a fully-automatic (based on error estimators), precise (respecting user-prescribed accuracies) and efficient (in terms of memory space and computational time) way. This algorithm is based on the multilevel Local Defect Correction (LDC) refinement approach. We first introduce an algorithmic extension of the LDC method to nonlinear quasi-static problems and provide key aspects associated with its practical implementation. Generic still open AMR-related questions associated with dynamic mesh adaptation, such as fields transfer between time steps and discretization error control over time, are then addressed. We propose a straightforward and efficient error non accumulation strategy lying on the introduction of the unbalance residual as an initial source term of the problem. Moreover, a reliable remeshing algorithm is introduced, aiming to limit the number of mesh regenerations over time while guaranteeing the fulfillment of user-prescribed errors. The efficiency of the proposed algorithm is demonstrated on several numerical experiments, in and , with different types of material behavior as well as evolving loads. Thanks to its natural ability to generate a hierarchy of meshes of limited sizes that dynamically follow the evolution over time of studied phenomena, the proposed extension of the LDC method clearly appears to be of great potential for many challenging applications.