  In this paper, we study the existence and uniqueness of weak solution of a
nonlinear poroelasticity model. To better describe the proccess of deformation
and diffusion underlying in the original model, we firstly reformulate the
nonlinear poroelasticity by a multiphysics approach. Then, we adopt the similar
technique of proving the well-posedness of nonlinear Stokes equations to prove
the existence and uniqueness of weak solution of a nonlinear poroelasticity
model. And we strictly prove the growth, coercivity and monotonicity of the
nonlinear stress-strain relation, give the energy estimates and use Schauder's
fixed point theorem to show the existence and uniqueness of weak solution of
the nonlinear poroelasticity model.
