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A physically motivated constitutive model for 3D numerical simulation of skeletal muscles
Author(s) -
Weickenmeier J.,
Itskov M.,
Mazza E.,
Jabareen M.
Publication year - 2014
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2618
Subject(s) - constitutive equation , finite element method , hyperelastic material , nonlinear system , cauchy stress tensor , tangent , computer science , mathematics , mathematical analysis , structural engineering , engineering , physics , geometry , quantum mechanics
SUMMARY A 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.