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 Omega 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, Omega is not equal to W in general.) The remaining part t(R) of the stress response does no work during loading. With biaxial testing, Omega can be definitively determined from data. Moreover, for tests with the stretch directions coaxial to the axes of anisotropy, t(R) can be accurately characterized by a scalar function omega that depends on the strain. This paper is part 1 of 2 with "I. Theory" and "II. Application."