The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.

中文翻译：

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拉伸皮肤：生理极限及超越。

本手稿的目标是建立一种新颖的皮肤计算模型，以表征其在超出其生理极限时的本构行为。在生理状态下，皮肤表现出可逆、高度非线性、拉伸锁定和各向异性行为。我们使用由八个蠕虫状链组成的横向各向同性链网络模型对这些特征进行建模。超出生理极限，皮肤会经历由机械拉伸引发的不可逆的区域生长。我们将皮肤生长建模为横向各向同性过程，通过单个内部变量（标量值生长乘数）来表征。为了离散时间增长的演化，我们应用了无条件稳定、隐式欧拉后向格式。为了在空间中离散化它，我们利用有限元方法。为了获得最大的算法效率和最佳的收敛性，我们建议使用内部牛顿迭代来局部更新每个积分点的增长乘数。该迭代嵌入外部牛顿迭代中，以全局更新每个有限元节点处的变形。为了说明皮肤生长的特征，我们首先比较位移驱动生长和力驱动生长的两个简单模型问题。然后，我们模拟组织扩张过程中拉伸诱导的皮肤生长过程。特别是，我们比较了四种常用组织扩张器几何形状的应力、应变和面积增益的时空演变。我们相信，所提出的模型有可能在重建手术中开辟新途径，并使组织扩张中的关键过程参数合理化，例如扩张器几何形状、扩张器尺寸、扩张器放置和充气时间。