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.

在本文中，我们开发了适用于许多组织（尤其是皮肤）的名义皮革材料的非弹性响应的二维膜模型。这些材料虽然名义上具有弹性，但在循环载荷下（通常称为Mullins型软化）显示出实质性和复杂的滞后响应。此外，它们在卸载时表现出速率依赖性行为和永久残余应变。所提出的模型基于多网络模型的概念，该模型由背景材料以及可能具有叠加响应的许多光纤家族组成。速率相关的非弹性和永久应变通过纤维打滑来建模。通过与大鼠和猪皮肤在各种循环负荷条件下的实验进行比较，我们显示了该模型的有效性。模态参数很容易直接从实验中测量。响应中纤维部分的关键成分是（1）简单的两斜率弹性响应，说明了纤维的快速硬化响应，松弛和刚性响应之间的平滑过渡代表了纤维的吸收（2）纤维的仿射变形，以解决纤维的滑移和恢复问题（3）快速硬化反应，以解决关于皮肤先前最大拉伸状态的记忆。整个框架以费率形式编写，可通过基本集成方案轻松实现。该模型不仅可以模拟皮肤的整体行为，而且还可以模拟内部轻微滞后。响应中纤维部分的关键成分是（1）简单的两斜率弹性响应，说明了纤维的快速硬化响应，松弛和刚性响应之间的平滑过渡代表了纤维的吸收（2）纤维的仿射变形以解决纤维的滑移和恢复（3）快速硬化反应，以解决与皮肤先前最大拉伸状态有关的记忆。整个框架以费率形式编写，可通过基本集成方案轻松实现。该模型不仅可以模拟皮肤的整体行为，而且还可以模拟内部轻微滞后。响应中纤维部分的关键成分是（1）简单的两斜率弹性响应，说明了纤维的快速硬化响应，松弛和刚性响应之间的平滑过渡代表了纤维的吸收（2）纤维的仿射变形以解决纤维的滑移和恢复（3）快速硬化反应，以解决与皮肤先前最大拉伸状态有关的记忆。整个框架以费率形式编写，可通过基本集成方案轻松实现。该模型不仅可以模拟皮肤的整体行为，而且还可以模拟内部轻微滞后。松弛和刚性响应之间具有平滑过渡，代表了纤维的补充（2）纤维的非仿射变形，以解决纤维的滑移和恢复（3）快速硬化的响应，以解决关于皮肤先前最大吸收的记忆拉伸状态。整个框架以费率形式编写，可通过基本集成方案轻松实现。该模型不仅可以模拟皮肤的整体行为，而且还可以模拟内部轻微滞后。在松弛和刚性响应之间具有平滑过渡，代表了纤维的补充（2）纤维的非仿射变形，以说明纤维的滑移和恢复（3）快速硬化的响应，以说明皮肤对先前最大吸收的记忆拉伸状态。整个框架以费率形式编写，可通过基本集成方案轻松实现。该模型不仅可以模拟皮肤的整体行为，而且还可以模拟内部轻微滞后。整个框架以费率形式编写，可通过基本集成方案轻松实现。该模型不仅可以模拟皮肤的整体行为，而且还可以模拟内部轻微滞后。整个框架以费率形式编写，可通过基本集成方案轻松实现。该模型不仅可以模拟皮肤的整体行为，而且还可以模拟内部轻微滞后。