Experimentally Tractable, Pseudo-elastic Constitutive Law for Biomembranes: I. Theory

Although visco-elastic in general, the stress-strain relation of biomembranes is one-to-one or pseudo-elastic when being loaded after preconditioning. This pseudo-elastic relation is hypoelastic (i.e., it is not hyperelastic), yet much of the stress response can be characterized by a scalar function Ω that represents the work done (per unit reference volume) on the specimen during loading. (Since a pseudo-strain-energy function W is optimized to fit the test data and not the work done, Ω is not equal to W in general.) The remaining part $tR$ of the stress response does no work during loading. With biaxial testing, Ω can be definitively determined from data. Moreover, for tests with the stretch directions coaxial to the axes of anisotropy, $tR$ can be accurately characterized by a scalar function ω that depends on the strain. This paper is part 1 of 2 with “I. Theory” and “II. Application.”