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Computational modeling of passive myocardium. (English) Zbl 1207.92006
Summary: This work deals with the computational modeling of passive myocardial tissue within the framework of mixed, nonlinear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscles. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model, which has originally been designed for exactly incompressible deformations, is extended towards entirely three-dimensional inhomogeneous deformations by additively decoupling the strain energy function into volumetric and isochoric parts along with the multiplicative split of the deformation gradient. This decoupled constitutive structure is then embedded in a mixed finite element formulation through a three-field Hu – Washizu functional whose simultaneous variation with respect to the independent pressure, dilatation, and placement fields results in the associated Euler-Lagrange equations, thereby minimizing the potential energy. This weak form is then consistently linearized for uniform-pressure elements within the framework of an implicit finite element method. To demonstrate the performance of the proposed approach, we present a three-dimensional finite element analysis of a generic biventricular heart model, subjected to physiological ventricular pressure. The parameters employed in the numerical analysis are identified by solving an optimization problem based on six simple shear experiments on explanted cardiac tissue.

MSC:
92C10 Biomechanics
74S05 Finite element methods applied to problems in solid mechanics
92C37 Cell biology
Software:
FEAP
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