Theoretical modeling of AC anisotropic mechanical properties
Articular cartilage (AC) is a COL fiber-reinforced composite that exhibits orthotropic behavior and asymmetric tensile-compressive responses and likely experiences finite deformations during in vivo and in vitro growth. Stress constitutive equations that accurately characterize the tissue’s mechanical properties must be developed in order to develop rigorous validation tests of our cartilage growth models.
In a series of studies, we have developed an anisotropic bimodular stress-strain equation for large strains to model the nonlinear AC response in tension and compression in three orthogonal directions. The model uses distinct collagen (COL) and glycosaminoglycan (GAG) stress equations. An anisotropic elastic COL network is modeled using fiber families that behave in a bimodular fashion; i.e. they only support tensile stresses. Two types of fiber families are introduced: primary fibers that are oriented along anatomical directions defined relative to the split-line direction (direction 1), and secondary fibers that represent crosslinking mechanisms between the primary fibers. The COL strain energy function satisfies polyconvexity conditions, resulting in numerical and material stability. For the GAGs, an isotropic elastic strain energy function is used based on an intra- and extra-fibrillar water compartment model that also satisfies polyconvexity.
Material constants are identified from our experimental results for newborn bovine AC. Results indicate that the theory has the capability to model anisotropic and asymmetric mechanical properties of AC determined from multi-directional tension and compression experiments. These models are then used to model growth with the cartilage growth mixture model and the cartilage growth finite element model.
Publications
- Klisch SM, Asanbaeva A, Oungoulian SR, Masuda K, Thonar EJ, Davol A, Sah RL. A cartilage growth mixture model with collagen remodeling: validation protocols. Journal of Biomechanical Engineering, 130:031006, 2008.ABSTRACT PDF
- Klisch SM. Bimodular polyconvex fiber-reinforced strain energy functions for articular cartilage. ASME Journal of Biomechanical Engineering, 129: 250-258, 2007.ABSTRACT PDF
- Klisch SM. A bimodular theory for finite deformations: comparison of orthotropic second-order and exponential stress constitutive equations for articular cartilage. Biomechanics and Modeling in Mechanobiology, 5:90-101, 2006.ABSTRACT PDF
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© 2008 Stephen M. Klisch | Mechanical Engineering