Poromechanics of saturated media based on the logarithmic finite strain

Abstract

In this paper, we introduce the mathematical formulation and numerical implementation of a coupled thermo-hydro-mechanical model for saturated poromaterials undergoing logarithmic finite deformation and corotational rates. The model combines (i) the thermodynamics of standard materials, (ii) the frame indifferent hyperelastoplasticty, (iii) the orthogonality condition of maximum dissipation, as well as (iv) the principles of conservations of mass, energy and momenta. This formulation involves new developments based on the logarithmic strain measures and corotational rates which overcome the aberrant oscillations classically encountered in large simple shear. It also takes into accounts recent findings on the thermodynamics of dissipative materials which consist of deriving the yielding conditions and flow rules from suitable free energy and dissipation functions. This framework resulted in the implementation of a new finite element algorithm based on Galerkin’s method. The numerical procedures used in this paper involve the spectral decomposition of the logarithmic strain measures, the gradient split techniques as well as the return mapping method. The formulation is validated using the classical problems of Terzaghi and strip loading consolidation.