FEM simulations for thixo-viscoplastic flow problems: wellposedness results

Abstract

In this contribution, we shall be concerned with the question of wellposedness of thixo viscoplastic flow problems in context of FEM approximations. We restrict our analysis to a quasi Newtonian modeling approach with the aim to set foundations for an efficient monolithic Newton multigrid solver. We present the wellposedness of viscoplastic subproblems and structure subproblems in parallel/independent fashion showing the possibility for a combined treatment. Then, we use the fixed point theorem for the coupled problem. For the numerical solutions, we choose 4:1 contraction config uration and use monolithic Newton-multigrid solver. We analyse the effect of taking into consideration thixotropic phenomena in viscoplastic material and opening up for more different coupling by inclusions of shear thickening and shear thinning behaviors for plastic viscosity and/or elastic behavior below the critical yield stress limit in more a general thixotropic models.