title: On the accuracy and fitting of transversely isotropic material models.
abstract: Fiber reinforced structures are central to the form and function of biological tissues. Hyperelastic, transversely isotropic material models are used widely in the modeling and simulation of such tissues. Many of the most widely used models involve strain energy functions that include one or both pseudo-invariants (I4 or I5) to incorporate energy stored in the fibers. In a previous study we showed that both of these invariants must be included in the strain energy function if the material model is to reduce correctly to the well-known framework of transversely isotropic linear elasticity in the limit of small deformations. Even with such a model, fitting of parameters is a challenge. Here, by evaluating the relative roles of I4 and I5 in the responses to simple loadings, we identify loading scenarios in which previous models accounting for only one of these invariants can be expected to provide accurate estimation of material response, and identify mechanical tests that have special utility for fitting of transversely isotropic constitutive models. Results provide guidance for fitting of transversely isotropic constitutive models and for interpretation of the predictions of these models.
authors.affiliation: School of Mechanical and Electronic Engineering, Soochow University, Suzhou, Jiangsu, China; Robotics and Microsystems Center, Soochow University, Suzhou, Jiangsu, China. Electronic address: fengyuan@suda.edu.cn.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Feng
authors.affiliation: Department of Mechanical Engineering and Materials Science, Washington University, St. Louis, MO, USA.
authors.forename: Ruth J
authors.initials: RJ
authors.lastname: Okamoto
authors.affiliation: Department of Mechanical Engineering and Materials Science, Washington University, St. Louis, MO, USA; Department of Neurological Surgery, Washington University, St. Louis, MO, USA; Department of Biomedical Engineering, Washington University, St. Louis, MO, USA.
authors.forename: Guy M
authors.initials: GM
authors.lastname: Genin
authors.affiliation: Department of Mechanical Engineering and Materials Science, Washington University, St. Louis, MO, USA; Department of Neurological Surgery, Washington University, St. Louis, MO, USA; Department of Biomedical Engineering, Washington University, St. Louis, MO, USA.
authors.forename: Philip V
authors.initials: PV
authors.lastname: Bayly
mesh_terms: D016880:Anisotropy; D001696:Biomechanical Phenomena; D003198:Computer Simulation; D004548:Elasticity; D008954:Models, Biological; D013314:Stress, Mechanical
keywords: Anisotropic material; Biological material; Constitutive behavior; Transversely isotropic constitutive model