Computational modeling can provide insight into understanding the damage mechanisms of soft biological tissues. Our gradient‐enhanced damage model presented in a previous publication has shown advantages in considering the internal length scales and in satisfying mesh independence for simulating damage, growth and remodeling processes. Performing sensitivity analyses for this model is an essential step towards applications involving uncertain patient‐specific data. In this paper, a numerical analysis approach is developed. For that we integrate two existing methods, that is, the gradient‐enhanced damage model and the surrogate model‐based probability analysis. To increase the computational efficiency of the Monte Carlo method in uncertainty propagation for the nonlinear hyperelastic damage analysis, the surrogate model based on Legendre polynomial series is employed to replace the direct FEM solutions, and the sparse grid collocation method (SGCM) is adopted for setting the collocation points to further reduce the computational cost in training the surrogate model. The effectiveness of the proposed approach is illustrated by two numerical examples, including an application of artery dilatation mimicking to the clinical problem of balloon angioplasty.

中文翻译：

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软生物组织非局部损伤的敏感性分析

计算建模可以深入了解软生物组织的损伤机制。我们在先前出版物中提出的梯度增强损伤模型在考虑内部长度尺度和满足网格独立性以模拟损伤、生长和重塑过程方面显示出优势。对该模型进行敏感性分析是迈向涉及不确定患者特定数据的应用的重要一步。在本文中，开发了一种数值分析方法。为此，我们整合了两种现有方法，即梯度增强损伤模型和基于代理模型的概率分析。为了提高蒙特卡罗方法在非线性超弹性损伤分析的不确定性传播中的计算效率，采用基于勒让德多项式级数的代理模型代替直接的有限元解法，并采用稀疏网格搭配方法（SGCM）设置搭配点，进一步降低训练代理模型的计算成本。所提出的方法的有效性通过两个数值例子来说明，包括动脉扩张模拟在球囊血管成形术的临床问题中的应用。