On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling
On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling
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DOI：
10.1016/j.cma.2022.114915
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发表时间：
2021-09
期刊：
影响因子：
--
通讯作者：
J. Fuhg;N. Bouklas
中科院分区：
文献类型：
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作者：
J. Fuhg;N. Bouklas
数据驱动的本构建模是计算固体力学的一个新兴领域，有望显着降低分层计算方法的计算成本。此外，这种数据驱动的范例可以实现探测材料响应的实验数据与结构层面的数值模拟的无缝连接。传统上，这些代理只是使用数据集进行训练，这些数据集将弹性和非弹性材料的应变输入直接映射到应力输出。最近，人工神经网络（ANN）经过训练，可以在构建这些模型时额外纳入基本物理定律。然而，从工程角度来看，人工神经网络不提供收敛保证，并且主要依赖于用户指定的参数。与 ANN 不同，高斯过程回归 (GPR) 基于非参数建模原理以及基础统计知识，因此可以提供严格的收敛保证。受到 Frankel 等人最近的工作的启发。 （2021）基于将应力输出重写为不可约完整性基础的线性组合，在这项工作中，我们提出了一种基于物理和数据驱动的本构建模方法，用于有限应变下各向同性和各向异性超弹性材料。经过训练的代理能够遵守物理原理，例如材料框架无关性、材料对称性、热力学一致性、无应力未变形配置以及角动量的局部平衡。我们的方法基于概率机器学习，可以独特地在大数据环境中使用，同时保持探地雷达的优势。由于混合不变空间中的采样提出了独特的挑战，我们另外提出了第一种采样方法，该方法直接在不变空间中生成与变形梯度张量的有界域相对应的空间填充点。采样技术基于模拟退火，提供更高效、更可靠的基于物理的本构模型。总体而言，所提出的方法在各向同性和各向异性本构定律的合成数据上进行了测试，并且显示出令人惊讶的准确性，甚至远远超出了训练领域的限制，这表明所产生的替代物可以有效地概括，因为它们结合了有关基础物理的知识。
Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. Additionally, this data-driven paradigm could enable a seamless connection of experimental data probing material responses with numerical simulations at the structural level. Traditionally, these surrogates have just been trained using datasets which map strain inputs to stress outputs for elastic and inelastic materials directly. Recently, artificial neural networks (ANNs) have instead been trained to additionally incorporate the underlying physical laws in the construction of these models. However, ANNs do not offer convergence guarantees from an engineering point of view and are majorly reliant on user-specified parameters. In contrast to ANNs, Gaussian process regression (GPR) is based on nonparametric modeling principles as well as on fundamental statistical knowledge and hence allows for strict convergence guarantees. Motivated by the recent work by Frankel et al. (2021) which is based on rewriting the stress output as a linear combination of an irreducible integrity basis, in this work we present a physics-informed and data-driven constitutive modeling approach for isotropic and anisotropic hyperelastic materials at finite strain. The trained surrogates are able to respect physical principles such as material frame indifference, material symmetry, thermodynamic consistency, stress-free undeformed configuration, and the local balance of angular momentum. Our approach is based on probabilistic machine learning and uniquely can be used in the big data context while maintaining the benefits of GPR. As sampling in the mixed invariant space poses a unique challenge, we additionally present the first sampling approach that directly generates space-filling points in the invariant space corresponding to a bounded domain of the deformation gradient tensor. The sampling technique is based on simulated annealing and provides more efficient and reliable physics-informed constitutive models. Overall, the presented approach is tested on synthetic data from isotropic and anisotropic constitutive laws and shows surprising accuracy even far beyond the limits of the training domain, indicating that the resulting surrogates can efficiently generalize as they incorporate knowledge about the underlying physics.