CI²MA - Publicaciones | Prepublicaciones

Pre-Publicación 2020-17

Patrick E. Farrell, Luis F. Gatica, Bishnu Lamichhane, Ricardo Oyarzúa, Ricardo Ruiz-Baier:

Mixed Kirchhoff stress - displacement - pressure formulations for incompressible hyperelasticity

Abstract:

We adapt the three-field formulation for nearly incompressible hyperelasticity introduced in [Chavan, Lamichhane, Wohlmuth, Comput. Methods Appl. Mech. Engrg. (2007), 196:4075{4086] to the fully incompressible case. We also discuss the solvability of the linearised problem restricted to simple material laws. We construct a mixed finite element scheme for simplicial meshes and verify its error decay through computational tests. We also propose a new augmented Lagrangian preconditioner that improves convergence properties of iterative solvers. A few benchmark solutions are computed, and we test the formulation in models of cardiac biomechanics using orthotropic strain energy densities.

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