On physics-informed data-driven isotropic and anisotropic constitutive models through probabilistic machine learning and space-filling sampling

by   Jan Niklas Fuhg, et al.

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. Traditionally, these surrogates have been trained using datasets which map strain inputs to stress outputs directly. Data-driven constitutive models for elastic and inelastic materials have commonly been developed based on artificial neural networks (ANNs), which recently enabled the incorporation of physical laws in the construction of these models. However, ANNs do not offer convergence guarantees and are 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. GPR however has the major disadvantage that it scales poorly as datasets get large. In this work we present a physics-informed data-driven constitutive modeling approach for isostropic and anisotropic materials based on probabilistic machine learning that can be used in the big data context. The trained GPR 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. Furthermore, this paper presents the first sampling approach that directly generates space-filling points in the invariant space corresponding to bounded domain of the gradient deformation tensor. 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.



There are no comments yet.


page 12


Tensor Basis Gaussian Process Models of Hyperelastic Materials

In this work, we develop Gaussian process regression (GPR) models of hyp...

Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks

Hierarchical computational methods for multiscale mechanics such as the ...

Thermodynamically Consistent Machine-Learned Internal State Variable Approach for Data-Driven Modeling of Path-Dependent Materials

Characterization and modeling of path-dependent behaviors of complex mat...

Drones Practicing Mechanics

Mechanics of materials is a classic course of engineering presenting the...

PEMNET: A Transfer Learning-based Modeling Approach of High-Temperature Polymer Electrolyte Membrane Electrochemical Systems

Widespread adoption of high-temperature polymer electrolyte membrane fue...

Data-Driven simulation of inelastic materials using structured data sets, tangent space information and transition rules

Data-driven computational mechanics replaces phenomenological constituti...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.