A closed-form structural model of planar fibrous tissue mechanics
Ramesh Raghupathy1, Victor H Barocas2
1Departments of Mechanical Engineering, University of Minnesota, Minneapolis, MN, United States.
Abstract:
Structural models of tissue mechanics, in which the tissue is represented as a sum or integral of fiber contributions for a distribution of fiber orientations, are a popular tool to represent the complex mechanical behavior of soft tissues. A significant practical challenge, however, is evaluation of the integral that defines the stress. Numerical integration is accurate but computationally demanding, posing an impediment to incorporation of structural models into large-scale finite-element simulations. In this paper, a closed-form analytic evaluation of the integral is derived for fibers distributed according to a von Mises distribution and an exponential fiber stress-strain law.
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