Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations
Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations
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DOI：
10.1016/j.cma.2023.116046
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发表时间：
2023-01
影响因子：
7.2
通讯作者：
Vahidullah Tac;M. Rausch;F. S. Costabal;A. B. Tepole
中科院分区：
文献类型：
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作者：
Vahidullah Tac;M. Rausch;F. S. Costabal;A. B. Tepole
我们开发了一个完全数据驱动的各向异性有限粘弹性模型，使用神经常微分方程作为积木。我们取代亥姆霍兹自由能函数和耗散潜力与数据驱动的功能，先验满足基于物理的约束，如客观性和热力学第二定律。我们的方法可以在三维任意载荷下模拟材料的粘弹性行为，即使是大变形和热力学平衡的大偏差。数据驱动的本质的管理潜力赋予模型非常需要的灵活性，在建模的粘弹性行为的广泛的一类材料。我们使用来自生物和合成材料（包括人脑组织，血凝块，天然橡胶和人类心肌）的应力-应变数据来训练模型，并表明数据驱动的方法优于传统的粘弹性封闭模型。
We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress–strain data from biological and synthetic materials including human brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.