A method based on Singular Value Decomposition (SVD) and Gaussian process machine learning is proposed to build a metamodel of a constitutive model that models time dependent and nonlinear behavior. To test this method, we apply it to determine the material parameters of a nonlinear viscoelastic (poly(vinylalcohol)) hydrogel (PVA). Using the metamodel, we are able to rapidly generate the stress histories for a large set of data points spanning a wide range of material parameters without solving the constitutive model of the PVA gel explicitly. To determine the material parameters, we compare the stress histories predicted by the metamodel with the observed stress histories from laboratory experiments consisting of uniaxial tension cyclic and relaxation tests. The efficiency of the metamodel allows us to determine the material parameters of the constitutive model governing the time-dependent behavior of the PVA gel in a short time. The proposed method shows that there exist many sets of material parameters that can faithfully reproduce the experimental data. Further, our method reveals important relationships between the material parameters in the constitutive model. Although the focus is on the PVA gel system, the method can be easily transferred to build a metamodel for any material model.

提出了一种基于奇异值分解 (SVD) 和高斯过程机器学习的方法来构建本构模型的元模型，该模型对时间相关和非线性行为进行建模。为了测试这种方法，我们应用它来确定非线性粘弹性（聚（乙烯醇））水凝胶 (PVA) 的材料参数。使用元模型，我们能够快速生成跨越各种材料参数的大量数据点的应力历史，而无需明确求解 PVA 凝胶的本构模型。为了确定材料参数，我们将元模型预测的应力历史与从实验室实验（包括单轴拉伸循环和松弛测试）中观察到的应力历史进行比较。元模型的效率使我们能够在短时间内确定控制 PVA 凝胶时间相关行为的本构模型的材料参数。所提出的方法表明存在许多组材料参数可以忠实地再现实验数据。此外，我们的方法揭示了本构模型中材料参数之间的重要关系。虽然重点是 PVA 凝胶系统，但该方法可以很容易地转移到为任何材料模型构建元模型。我们的方法揭示了本构模型中材料参数之间的重要关系。虽然重点是 PVA 凝胶系统，但该方法可以很容易地转移到为任何材料模型构建元模型。我们的方法揭示了本构模型中材料参数之间的重要关系。虽然重点是 PVA 凝胶系统，但该方法可以很容易地转移到为任何材料模型构建元模型。