A multinetwork inelastic model for the hysteretic response during cyclic loading of pig and rat skin

Abstract

In this paper, we develop a 2-dimensional membrane model for the inelastic response of nominally leathery materials applicable to many tissues, particularly skin. These materials, while nominally elastic, show substantial and complex hysteretic response under cyclic loading (usually referred to as the Mullins-type softening). Furthermore, they exhibit both rate dependent behavior and permanent residual strain upon unloading. The proposed model is based on the notion of a multinetwork model composed of a background material and possibly many families of fibers with a superposed response. The rate dependent inelasticity and permanent strain are modeled through fiber slippage. We show the efficacy of the model by comparing with experiments in rat and pig skin under various cyclic loading conditions. The parameters of the modal are reasonably easy to measure directly from experiments. The key ingredients of the fiber part of the response are (1) a simple two-slope elastic response that accounts for the rapid stiffening response of the fibers, with smooth transition between the slack and stiff response representing the fiber recruitment (2) a non affine deformation of the fibers to account for the fiber slippage and recovery (3) a rapidly hardening response to account for the memory of the skin regarding its previous maximum stretched state. The entire framework is written in rate form and is easily implemented with an elementary integration scheme. The model is capable of simulating not only the overall behavior of the skin but internal minor hysteresis as well.