Data-driven modeling of the mechanical behavior of anisotropic soft biological tissue
Data-driven modeling of the mechanical behavior of anisotropic soft biological tissue
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DOI：
10.1007/s00366-022-01733-3
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发表时间：
2021-07
影响因子：
8.7
通讯作者：
Vahidullah Tac;V. Sree;M. Rausch;A. B. Tepole
中科院分区：
文献类型：
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作者：
Vahidullah Tac;V. Sree;M. Rausch;A. B. Tepole
封闭本构模型是目前描述软组织力学行为的标准方法。然而，这种方法存在固有的缺陷。例如，显式函数形式可能导致较差的拟合度、不唯一的拟合度以及对参数的夸大敏感性。在这里，我们通过设计深度神经网络(DNN)来取代这种显式的专家模型，从而克服了其中的一些问题。在这种情况下使用DNN的一个挑战是强制执行压力客观性。我们通过训练我们的DNN来根据(伪)不变量预测应变能及其导数来应对这一挑战。因此，我们还可以通过对损失函数中应变能及其导数的物理信息约束来加强多凸性。能量和导数函数的直接预测也使得有限元实现所需的弹性张量的计算成为可能。然后，我们通过从双轴测试数据中学习猪和小鼠皮肤的各向异性力学行为来展示DNN的能力。通过这个例子，我们发现高保真实验数据和低保真分析近似相结合的多保真方案产生了最好的性能。最后，我们使用我们的DNN模型进行了组织扩张的有限元模拟，以说明像我们这样的数据驱动方法在医疗器械设计中的潜力。此外，我们期待这项工作所产生的开放数据和软件将扩大数据驱动的本构模型在软组织力学中的应用。
Closed-form constitutive models are currently the standard approach for describing soft tissues’ mechanical behavior. However, there are inherent pitfalls to this approach. For example, explicit functional forms can lead to poor fits, non-uniqueness of those fits, and exaggerated sensitivity to parameters. Here we overcome some of these problems by designing deep neural networks (DNN) to replace such explicit expert models. One challenge of using DNNs in this context is the enforcement of stress-objectivity. We meet this challenge by training our DNN to predict the strain energy and its derivatives from (pseudo)-invariants. Thereby, we can also enforce polyconvexity through physics-informed constraints on the strain-energy and its derivatives in the loss function. Direct prediction of both energy and derivative functions also enables the computation of the elasticity tensor needed for a finite element implementation. Then, we showcase the DNN’s ability by learning the anisotropic mechanical behavior of porcine and murine skin from biaxial test data. Through this example, we find that a multi-fidelity scheme that combines high fidelity experimental data with a low fidelity analytical approximation yields the best performance. Finally, we conduct finite element simulations of tissue expansion using our DNN model to illustrate the potential of data-driven approaches such as ours in medical device design. Also, we expect that the open data and software stemming from this work will broaden the use of data-driven constitutive models in soft tissue mechanics.