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Abstract: Poroelasticity has many applications in energy, environmental engineering, and even biomedicine. When linear, it simulates the transient flow of a single-phase fluid in a deformable linear elastic porous medium. However, when the medium is brittle and fractured, linear elasticity is not applicable, but new nonlinear implicit models of elasticity lead to a good description of the phenomenon. I shall introduce for beginners the simplest model of poroelasticity, then describe some new implicit nonlinear models and explain their mathematical and numerical issues.

Collaborators: Tameem Almani, Andrea Bonito, Saumik Dana, Benjamin Ganis, Maria Gonzalez Taboada, Diane Guignard, Frederic Hecht, Kundan Kumar, Xueying Lu, Marc Mear, Kumbakonam Rajagopal, Gurpreet Singh, Endre Suli, Mary Wheeler.