A strain energy function for finite deformations is developed that has the capability to describe the nonlinear, anisotropic, and asymmetric mechanical response that is typical of articular cartilage. In particular, the bimodular feature is employed by including strain energy terms that are only mechanically active when the corresponding fiber directions are in tension. Furthermore, the strain energy function is a polyconvex function of the deformation gradient tensor so that it meets material stability criteria. A novel feature of the model is the use of bimodular and polyconvex “strong interaction terms” for the strain invariants of orthotropic materials. Several regression analyses are performed using a hypothetical experimental dataset that captures the anisotropic and asymmetric behavior of articular cartilage. The results suggest that the main advantage of a model employing the strong interaction terms is to provide the capability for modeling anisotropic and asymmetric Poisson’s ratios, as well as axial stress–axial strain responses, in tension and compression for finite deformations.
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April 2007
Technical Papers
A Bimodular Polyconvex Anisotropic Strain Energy Function for Articular Cartilage
Stephen M. Klisch
Stephen M. Klisch
Associate Professor
Mechanical Engineering Department,
e-mail: sklisch@calpoly.edu
California Polytechnic State University
, San Luis Obispo, CA 93407
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Stephen M. Klisch
Associate Professor
Mechanical Engineering Department,
California Polytechnic State University
, San Luis Obispo, CA 93407e-mail: sklisch@calpoly.edu
J Biomech Eng. Apr 2007, 129(2): 250-258 (9 pages)
Published Online: September 15, 2006
Article history
Received:
May 1, 2006
Revised:
September 15, 2006
Citation
Klisch, S. M. (September 15, 2006). "A Bimodular Polyconvex Anisotropic Strain Energy Function for Articular Cartilage." ASME. J Biomech Eng. April 2007; 129(2): 250–258. https://doi.org/10.1115/1.2486225
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