Development and Calibration of 3D Constitutive Equations for Nonlinear Passive Multi-Axial Finite Deformations of Skeletal Muscles

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 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 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 using a 3D model, different modes of deformations of skeletal muscle such as simple tension, biaxial and 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. Also, the model results are compared with the ones from two well- known hyper elastic Ogden and Mooney-Rivilin models in order to show the priority of the new developed 3D model to those aforementioned models has been shown.