Convex Fung-type potentials for biological tissues |
| |
Authors: | Salvatore Federico Alfio Grillo Gaetano Giaquinta Walter Herzog |
| |
Institution: | (1) Human Performance Laboratory, Faculty of Kinesiology, The University of Calgary, 2500 University Drive NW, Calgary, AB, T2N 1N4, Canada;(2) Dipartimento di Metodologie Fisiche e Chimiche per l’Ingegneria, Facoltà di Ingegneria, Università di Catania, Viale Andrea Doria 6, 98125 Catania, Italy;(3) Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, Sezione di Catania, Viale Andrea Doria 6, 98125 Catania, Italy |
| |
Abstract: | The anisotropic, non-linear elastic behavior of biological soft tissue is typically accounted for by the hypothesis of hyperelasticity,
i.e., the existence of an elastic potential. Fung-type potentials, based on the exponential of a quadratic form in the components
of the Green-Lagrange strain, have been widely used in soft tissue modeling, and have inspired potentials in which the exponential
was replaced by other monotonically increasing functions. It has been shown that simple fitting of the parameters of a Fung-type
potential to experimental stress-strain curves may lead to non-convexity, with undesirable effects on the reliability of the
algorithms used in Finite Element simulations. In this paper, we prove that the necessary and sufficient condition for the
strict convexity of a Fung-type potential is that the quadratic form in the exponential is positive definite. This result
provides a clear physical meaning for the parameters featuring in the quadratic form, and their relationship with the small-strain
elastic moduli. This consistency relationship must be respected in order to guarantee that the Fung-type potential correctly
reduces to the quadratic potential of classic linear elasticity in the small-strain approximation. Furthermore, we show that,
when the conditions of convexity and consistency with the linear theory are respected, Fung-type potentials become a one-parameter
family, and we discuss the consequences of this result for when fitting experimental data.
An erratum to this article can be found at |
| |
Keywords: | Elasticity Anisotropy Convexity Biological tissue Continuum mechanics |
本文献已被 SpringerLink 等数据库收录! |
|