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

TL;DR

This paper develops and tests two-scale numerical algorithms for modeling stress-strain behavior in porous media with self-contact at the pore level, combining homogenization theory and iterative micro-macro contact problem solutions.

Contribution

It introduces new two-scale algorithms for porous media with self-contact, including a dual micro-level formulation and iterative solution strategies.

Findings

Algorithms effectively model self-contact in porous media.

Numerical examples demonstrate the algorithms' applicability.

Micro- and macro-level contact solutions are successfully integrated.

Abstract

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, rigid inclusion 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 take 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.