Metamodeling of constitutive model using Gaussian process machine learning

• Published in: Journal of the mechanics and physics of solids 2021-09, Vol.154, p.104532, Article 104532
• Main Authors: Wang, Jikun, Li, Tianjiao, Cui, Fan, Hui, Chung-Yuen, Yeo, Jingjie, Zehnder, Alan T.
• Format: Article
• Language: English
• Subjects: Constitutive models; Data points; Gaussian process; Hydrogels; Machine learning; Metamodels; Parameter fitting; Parameters; PVA hydrogel; Singular value decomposition; Stress relaxation tests; Time dependence; Viscoelastic model
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2021.104532

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.