Minimization principles in poro-hydro-elasticity at fracture and their exploitation

Abstract eng:
The goal of this work is twofold. First, a minimization principle for the evolution problem of Biot-type poro-hydro-elasticity is developed [5]. It does not only have the advantage of a compact canonical notation that emphasizes symmetries. The displacement-flux prin- ciple obtained can be exploited by a new unconstrained stable finite element design, while space discretizations of standard displacement- pressure saddle point principle are constrained by the LBB condition. Second goal is the coupling of the variational model for poro-hydro- elasticity with fracture. This is done by a recently developed phase field approach [1, 5] that regularizes sharp crack discontinuity. In this multi-physics scenario, specific attention has to be paid to the crack growth function as well as extra treatment of fluid flow inside of cracks.

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