A mathematical modeling for in vitro skeletal muscle behavior in shear deformation modes

Skeletal muscles simulation remains a controversial topic as a result of its complex anatomical structure and mechanical characteristics such as nonlinear material properties and loading conditions. Most of the current models in the literature for describing the constitutive equations of skeletal muscles are based on Hill's one-dimensional, three element model. In this paper a 3D constitutive model which is based on the non-linear hyper elastic behavior of skeletal muscle and energy function has been presented. By using the derivatives of such energy function for defining the Second Piola and Cauchy stresses, we are able to describe the inactive behavior of skeleton muscles. The applied constitutive equations are an efficient generalization of Hamphury's model for the inactive behavior of skeletal muscle. In this paper by using a 3D model, different modes of deformations of skeletal muscle in the shear tests has been investigated and material properties constants for each modes of deformation has been optimized by Genetic algorithm. Finally the results of the model simulations of each mode are compared with those obtained from experimental tests.