Preprint 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.
This preprint gave rise to the following definitive publication(s):
Patrick E. FARRELL, Luis F. GATICA, Bishnu LAMICHHANE, Ricardo OYARZúA, Ricardo RUIZ-BAIER: Mixed Kirchhoff stress - displacement - pressure formulations for incompressible hyperelasticity. Computer Methods in Applied Mechanics and Engineering, vol. 374, Art. Num. 113562, (2021).