Measure-valued loads for a hyperelastic model of soft tissues

We study a simplified version of a class of constitutive relations used to describe large deformations of soft tissues, where the elastic energy density involves an exponential term. The class was originally introduced by Y.C. Fung as a model of many biological soft tissues in a series of papers during the Seventies. We prove existence and uniqueness of the equilibrium solution for a general measure-valued external load, under quite general boundary conditions, and study the validity of the associated Euler–Lagrange equation in the sense of distributions.