Mixed-dimensional poromechanical models of fractured porous media

TL;DR

This paper develops mixed-dimensional poromechanical models for fractured porous media, integrating continuum mechanics with new calculus for fractured systems, addressing both linear and non-linear behaviors, and establishing well-posedness under certain conditions.

Contribution

It introduces a novel framework combining classical mechanics with mixed-dimensional calculus for fractured media, including models with non-linear laws and mathematical well-posedness analysis.

Findings

Models are formulated for both finite and infinitesimal strains.

Non-linear constitutive laws like friction and contact are incorporated.

Well-posedness is proven for the infinitesimal strain case under specific assumptions.

Abstract

We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations for flow in, and deformation of, fractured materials. We present models both in the context of finite and infinitesimal strain, and discuss non-linear (and non-differentiable) constitutive laws such as friction models and contact mechanics in the fracture. Using the theory of well-posedness for evolutionary equations with maximal monotone operators, we show well-posedness of the model in the case of infinitesimal strain and under certain assumptions on the model parameters.