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arXiv · 2112.05038

Mixed-dimensional poromechanical models of fractured porous media

Wietse M. Boon·Jan M. Nordbotten
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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.

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Wietse M. Boon, Jan M. Nordbotten. 2021-12-09. Mixed-dimensional poromechanical models of fractured porous media. https://arxiv.org/abs/2112.05038

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