LAUSR

Abstract A Green-elastic response function based on a non-algebraic invariant representation for the in-plane deformation of tissue (porcine skin) is developed. It retains orthotropy and simulates the characteristic bimodal behavior (a very low modulus regime followed by a rapidly stiffening response) with experimentally determinable and meaningful parameters. This is achieved by using a recently developed upper triangular (or QR decomposition) of the deformation gradient using the orthotropy axes and defining physically meaningful ‘equivalent strains’ that are non-algebraic functions of the usual invariants. We demonstrate that the strain energy density can be written as a function of one or more such ‘equivalent strains’ and can be used to model the orthotropic response of such bimodal materials. The model is used to simulate the orthotropic unload-reload response of porcine-skin when loaded in different directions with results that compare well with experiments based on a single orthotropic-equivalent strain measure.