An elasto-visco-plastic model using the finite element method for crustal and lithospheric deformation

A novel numerical model based on solid deformation is presented in this paper. This thermo-mechanical model can simulate the tectonic evolution of crust and (lithospheric and asthenospheric) mantle under different conditions. Our implementation uses the finite element method (FEM) in order to solve the equations. As a Lagrangian approach is employed, remeshing techniques are implemented to avoid distortion problems when a certain deformation threshold is reached. The translation of the state between the old and new mesh is achieved by means of the information stored on Lagrangian particles, which minimizes the diffusion. The model is able to represent elastic, viscous and plastic behaviour inside the studied domain. Three types of creep mechanism (diffusion, dislocation and Peierls) are included. Two different quadrilateral isoparametric elements were implemented and can be employed to perform the calculations. The first one is an element with 4 nodes, selective reduced integration and a stabilization operator to diminish hourglass modes, which reduces the computational time needed. The second one has 8 nodes located in standard positions, uses full integration scheme and has no hourglass modes as it satisfies the Inf-Sup condition. Several test cases with known solutions were run to validate the different aspects of the implementation.