Recent studies in mammalian hearts show that left ventricular wall thickening
is an important mechanism for systolic ejection and that during contraction the
cardiac muscle develops significant stresses in the muscular cross-fiber
direction. We suggested that the collagen network surrounding the muscular
fibers could account for these mechanical behaviors. To test this hypothesis we
develop a model for large deformation response of active, incompressible,
nonlinear elastic and transversely isotropic living soft tissue (such as
cardiac or arteries tissues) in which we include a coupling effect between the
connective tissue and the muscular fibers. Then, a three-dimensional finite
element formulation including this internal pseudo-active kinematic constraint
is derived. Analytical and finite element solutions are in a very good
agreement. The numerical results show this wall thickening effect with an order
of magnitude compatible with the experimental observations
