A review on data-driven constitutive laws for solids

TL;DR

This review addresses data-driven constitutive modeling for solids, covering both path-independent elasticity and path-dependent plasticity, viscoelasticity, and damage/fracture. It introduces a taxonomy that divides ML-based and model-free approaches and contrasts interpretable symbolic methods with black-box neural networks, while stressing the incorporation of physics constraints and thermodynamic consistency. The authors discuss data sampling, design of experiments, verification, and validation as critical challenges and propose a data-availability-aware roadmap for reconciling theory with practice. They also highlight the need for robust uncertainty quantification, experimental–computational integration, and community benchmarks to accelerate trustworthy data-driven constitutive modeling.

Abstract

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits and drawbacks of the various techniques for interpreting and forecasting mechanics behavior across different scales. Distinguishing between machine-learning-based and model-free methods, we further categorize approaches based on their interpretability and on their learning process/type of required data, while discussing the key problems of generalization and trustworthiness. We attempt to provide a road map of how these can be reconciled in a data-availability-aware context. We also touch upon relevant aspects such as data sampling techniques, design of experiments, verification, and validation.

Figures (7)

• Figure 1: Characteristic features of the approaches in the constitutive modeling context.
• Figure 2: Different one-shot sampling strategies. (a) Grid sampling. The input domain is discretized using equidistant samples. (b) Uniform sampling. The sample points are generated from a uniform distribution in the input domain. (c) Latin hypercube sampling. The points are sampled such that there is only one point at each section of a divided input space.
• Figure 3: First NN architectures based on quasi-sequential data used for stress-controlled path-dependent modeling of concrete inspired by ghaboussi1991knowledge.
• Figure 4: TANNs proposed by masi2021thermodynamics
• Figure 5: Modular elastoplastic material modeling. The initial yielding can be fully DD or can separately include the equivalent stress measure and the yield stress. Hardening components can e.g. include the deformation resistance or some form of hardening moduli. See vlassis2022component and fuhg2023modular.