Taç Vahidullah, Rausch Manuel, Costabal Francisco Sahli, Tepole Adrian Buganza
Department of Mechanical Engineering, Purdue University, West Lafayette, IN, USA.
Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, Austin, TX, USA.
Comput Methods Appl Mech Eng. 2023 Jun 1;411. doi: 10.1016/j.cma.2023.116046. Epub 2023 Apr 21.
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 humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.
我们使用神经常微分方程作为构建模块，开发了一个完全数据驱动的各向异性有限粘弹性模型。我们用先验满足诸如客观性和热力学第二定律等基于物理的约束条件的数据驱动函数，取代了亥姆霍兹自由能函数和耗散势。我们的方法能够对材料在任意载荷下的三维粘弹性行为进行建模，即使存在大变形和与热力学平衡的大偏差。控制势的数据驱动性质赋予了该模型在对广泛材料的粘弹性行为进行建模时急需的灵活性。我们使用来自生物和合成材料（包括人脑组织、血凝块、天然橡胶和人体心肌）的应力-应变数据对模型进行训练，并表明数据驱动方法优于传统的粘弹性封闭形式模型。
