Abstract: In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation. Firstly, we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields. Secondly, a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically. Thirdly, existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically. Lastly, numerical tests are given to verify the theoretical results.

Key words: Nonlinear poroelasticity model, Multiphysics finite element method, Backward Euler method