A physically motivated constitutive model for 3D numerical simulation of skeletal muscles

SUMMARYA detailed numerical implementation within the FEM is presented for a physically motivated three‐dimensional constitutive model describing the passive and active mechanical behaviors of the skeletal muscle. The derivations for the Cauchy stress tensor and the consistent material tangent are provided. For nearly incompressible skeletal muscle tissue, the strain energy function may be represented either by a coupling or a decoupling of the distortional and volumetric material response. In the present paper, both functionally different formulations are introduced allowing for a direct comparison between the coupled and decoupled isochoric‐volumetric approach. The numerical validation of both implementations revealed significant limitations for the decoupled approach. For an extensive characterization of the model response to different muscle contraction modes, a benchmark model is introduced. Finally, the proposed implementation is shown to provide a reliable tool for the analysis of complex and highly nonlinear problems through the example of the human mastication system by studying bite force and three‐dimensional muscle shape changes during mastication. Copyright © 2014 John Wiley & Sons, Ltd. The mechanical behavior of skeletal muscle is described by physically based nearly incompressible constitutive equations and is implemented for finite element simulations of passive and active muscle responses. Unphysical volume growth was observed when formulating the strain energy function on the basis of ‘decoupled’ distortional‐volumetric contributions while the model performed well for the ‘coupled’ case. Numerical examples including a detailed reconstruction of the human mastication system demonstrate reliability and good predictive capabilities of the model with respect to the muscle force and 3D shape changes.