On Tuesday December 3, 2019 Prof. Hans van Duijn from TU Eindhoven will give a SFB 1313 Lecture about "On the Equations of Nonlinear Single-Phase Poroelasticity".
Date: December 3, 2019
Time: 4 pm
Place: MML (U 1.003), Pfaffenwaldring 61
Title: "On the Equations of Nonlinear Single-Phase Poroelasticity"
We discuss the equations of nonlinear poroelasticity derived from mixture theory. They describe the quasi-static mechanical behaviour of a fluid saturated porous medium. The nonlinearity arises from the compressibility of the fluid and from the dependence of porosity and permeability on the volume strain. We point out some limitations of the model. In our approach we discretize the quasi-static formulation in time and first consider the incremental problem. For this we prove existence using Brezis' theory of pseudo-monotone operators. Generalizing Biot's free energy to the nonlinear setting we construct a Lyapunov functional. This allows us to obtain bounds that are uniform with respect to the time step, yielding global stability. In the case when dissipative interface effects between fluid and solid are present, we consider the continuous time case in the limit when the time step tends to zero. This yields existence of a weak free energy solution. This is joint work with Andro Mikelic from the Institut Camille Jordan, Université Lyon 1, France.