A new monolithic Newton-multigrid-based FEM solution scheme for large strain dynamic poroelasticity problems

This paper presents a new efficient monolithic finite element solution scheme to treat the set of PDEs governing a two-dimensional, biphasic, saturated TPM model with intrinsically coupled and incompressible solid and fluid constituents for infinitesimal and large elastic deformation. Our approach, which inherits some of its techniques from CFD, is characterized by the following aspects: (1) It only performs operator evaluation with no additional Gateaux derivatives. In particular, the computations of the time-consuming material tangent matrix are not involved here; (2) It solves the non-linear dynamic problem with no restriction on the strength of coupling; (3) It is more efficient than the linear uvp solver discussed in previous works; (4) It requires weaker derivatives and hence lower order FE can be tested; (5) The boundary conditions are reduced, solution independent and more convenient to apply than in the old uvp formulation. For the purpose of validation and comparison, prototypical simulations including analytical solutions are carried out and at the end, an adaptive time stepping (ATS) procedure is introduced to handle the rapid change in the numbers of non-linear iterations that may occur