An active strain formulation for orthotropic
constitutive laws arising in cardiac mechanics modeling
is introduced and studied. The passive mechanical
properties of the tissue are described by the
Holzapfel-Ogden relation. In the active strain
formulation, the Euler-Lagrange equations for minimizing
the total energy are written in terms of active and
passive deformation factors, where the active part is
assumed to depend, at the cell level, on the
electrodynamics and on the specific orientation of the
cardiac cells. The well-posedness of the linear system
derived from a generic Newton iteration of the original
problem is analyzed and different mechanical activation
functions are considered. In addition, the active strain
formulation is compared with the classical active stress
formulation from both numerical and modeling
perspectives. Taylor-Hood and MINI finite elements are
employed to discretize the mechanical problem. The
results of several numerical experiments show that the
proposed formulation is mathematically consistent and is
able to represent the main key features of the
phenomenon, while allowing savings in computational
costs.