Numerical modelling of nonlinear behaviour of soft biological materials

Biological materials such as, for instance, the human skin, brain tissue, papillary muscles, and arteries are often characterized as nonlinear elastic materials. Various attempts at characterizing a strain-energy density function for such materials have been made.1-4 In normal physiological functioning, as well as in inadvertent circumstances such as injuries, these materials are subject to finite strains. For instance, as estimated in Danielson,’ the skin over the middle joint of a finger elongates about 20% when the joint is bent. Likewise, 5,6 the brain tissue may be subjected to strains of the order of 30% in situations of head injury. This paper presents a summary of recent studies by the authors7-9 that deal with consistent and rigorous numerical methods for modelling such finite deformation problems, as above, for biological materials of the nonlinear elastic incompressible type. Due to space limitations, the presentation is necessarily cursory; further details may be found elsewhere.7-g The formulations presented are valid for an incompressible nonlinear elastic material with any general strain energy density function; specific forms of such strain energy functionsl-4 can be implemented in a straightforward manner.