Jeffrey E. Bischoff, Ellen M. Arruda, and Karl Grosh
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Michigan, USA
Skin possesses material anisotropy due to preferred fiber alignment in the skin. This alignment results from prolonged exposure to a surrounding stress state. Previous attempts to model skin have generally used isotropic hyperelastic laws. We develop an anisotropic hyperelastic constitutive law for skin, based on an anisotropic unit cell of collagen fibers. Anisotropy is described mathematically by specifying the preferred fiber orientation throughout the domain. The behavior of the collagen chains is governed by the statistical mechanics of long chain molecules as characterized by a fiber density and a locking stretch, beyond which the fibers cannot extend. Additionally, by allowing the preferred fiber orientation and the chain properties (such as length) to evolve with time and the applied stress, skin growth can be described. This model has been incorporated into finite element code to simulate experiments in the literature that demonstrate material anisotropy and growth.