Abstract: Soft biological tissues are complicated, highly functional natural structures. The distribution, arrangement and interaction of their constituents lead to a diversity of mechanical properties like e.g. strong anisotropy, highly non-linear behavior, the ability to undergo large elastic strains or deformation induced softening in the form of preconditioning. Facing this variety, development and application of constitutive models is not a trivial task and many methods successfully applied to engineering materials fail to describe biological tissues adequately.
Besides the requirements from a biological perspective, any appropriate constitutive model is expected to yield physically reasonable results. When mechanical boundary value problems are considered, the existence of a solution is desired. Thereby, the issue of material stability also plays an important role. For hyperelastic materials, both these conditions can be fulfilled if the strain energy function is polyconvex and coercive. We propose a generalized polyconvex anisotropic strain energy function represented by a series with an arbitrary number of terms. Each term of this series a priori satisfies the condition of the energy and stress free natural state. The collagen fiber alignment is taken into account by means of structural tensors, where orthotropic and transversely isotropic material symmetries appear as special cases. The model has successfully been applied to simulate rabbit skin, bovine pericardium, porcine myocardium, human aortic and other arterial tissues.
For material characterization, biological tissues are usually tested in a preconditioned state. However, when living tissues are considered, the virgin response and preconditioning behavior itself can become crucial. For example, the mechanical behavior of human organs during surgery corresponds rather to a virgin than to a preconditioned state. The phenomenon of preconditioning is taken into account by an evolution of material parameters in the proposed hyperelastic model. The well-known Mullins effect can be obtained as a special case of this approach.