Homogenization and numerical algorithms for two-scale modeling of porous media with self-contact in micropores

The paper presents two-scale numerical algorithms for stress–strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic skeleton and a void pore. Unilateral frictionless contact is considered between opposing surfaces of the pore. For the homogenized model derived in our previous work, we justify incremental formulations and propose several variants of two-scale algorithms which commute iteratively solving of the micro- and the macro-level contact subproblems. A dual formulation which takes advantage of the assumed microstructure periodicity and a small deformation framework, is derived for the contact problems at the micro-level. This enables to apply the semi-smooth Newton method. For the global, macrolevel step two alternatives are tested; one relying on a frozen contact identified at the microlevel, the other based on a reduced contact associated with boundaries of contact sets. Numerical examples of 2D deforming structures are presented as a proof of the concept. •A new two-scale variational method for unilateral self-contact in porous media is derived.•The proposed incremental formulation uses a consistent homogenized elastic tensor.•The new macroscopic contact method couples micro- and macro-scopic contact problems.•A dual formulation is proposed to solve local contact microproblems efficiently.•The presented model and solution method are easily extensible to fluid-filled pores.