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

• Published in: International journal of non-linear mechanics Vol. 126; p. 103555
• Main Authors: Afsar Kazerooni, N., Srinivasa, A.R., Criscione, J.C.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01-11-2020; Elsevier BV
• Subjects: Cyclic loads; Elasticity; Fiber recruitment; Fiber slippage; Fibers; Hysteresis; Inelastic behavior; Mullins effect; Multinetwork model; Non-affine deformation; Pigskins; Rate dependence; Skin; Skin response; Stiffening; Two dimensional models; Non-affine deformation; Fiber recruitment; Fiber slippage; Skin response; Skin; Mullins effect; Multinetwork model; Inelastic behavior; Rate dependence
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2020.103555

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.
•Fibrous Soft materials and soft tissue retain orthotropy and show bimodal behavior with two different asymptotic moduli during unloading and reloading. This is due to the presences of many fiber families that are initially slack and stretch during deformation.•Inelasticity of skin is do to fiber slippage and later reattachment.•Our experiments on partial unloading and reloading of the cyclic response of skin shows rate independent irreversible response which can be partially recovered over long periods of time. This has not been reported by researchers in the field.•Rather than using complicated history integral approaches to model inelasticity, motivated by the microstructural response, we introduce non-affine deformations of the fiber and write a rate equation for the difference between the total strain and the fiber strain.•This leads to quite a simple response with easily identifiable parameters that can be discretized and simulated easily unlike the history integral approach.•The model is capable of simulating the response of porcine and pig skin when loaded in different directions and comparisons with data show excellent agreement for cyclic loading.