A Membrane Model from Implicit Elasticity Theory: Application to Visceral Pleura

Freed, A. D., Liao, J., & Einstein, D. R. (2014). A Membrane Model from Implicit Elasticity Theory: Application to Visceral Pleura. Biomechanics and Modeling in Mechanobiology. 13(4), 871-881. DOI:DOI 10.1007/s10237-013-0542-8.

Abstract

A Fungean solid is derived for membranous materials as a body defined by isotropic response functions whose mathematical structure is that of a Hookean solid where the elastic constants are replaced by functions of state derived from an implicit, thermodynamic, internal energy function. The theory utilizes Biot’s (Lond Edinb Dublin Philos Mag J Sci 27:468–489, 1939) definitions for stress and strain that, in one-dimension, are the stress/strain measures adopted by Fung (Am J Physiol 28:1532–1544, 1967) when he postulated what is now known as Fung’s law. Our Fungean membrane model is parameterized against a biaxial data set acquired from a porcine pleural membrane subjected to three, sequential, proportional, planar extensions. These data support an isotropic/deviatoric split in the stress and strain-rate hypothesized by our theory. These data also demonstrate that the material response is highly nonlinear but, otherwise, mechanically isotropic. These data are described reasonably well by our otherwise simple, four-parameter, material model.