What question did this study set out to answer?

This work aims to integrate Bayesian inference into constitutive modeling for plasticity and damage mechanics to improve uncertainty quantification and computational efficiency.

March 25, 2026

Hierarchical Bayesian inference for multiscale plasticity and damage with neural network surrogate models

Key Points

This work aims to integrate Bayesian inference into constitutive modeling for plasticity and damage mechanics to improve uncertainty quantification and computational efficiency.
Developed a hierarchical Bayesian approach for inferring material parameters.
Embedded deterministic constitutive models into a probabilistic framework to handle random material variables.
Formulated Bayesian inverse problems with likelihood functions from mechanical data including cyclic loading.
Employed neural-network-based surrogate models to evaluate likelihoods and facilitate efficient posterior sampling.
Achieved up to two orders of magnitude reduction in computational time compared to direct finite element simulations.
Maintained high predictive accuracy with root-mean-square errors below 1% in surrogate-based inference.
Demonstrated improved identifiability of parameters and consistent uncertainty bounds on stress-strain relationships.

Abstract

The integration of Bayesian inference into constitutive modeling provides a rigorous framework for uncertainty quantification in plasticity and damage mechanics. This work presents a hierarchical Bayesian approach for inferring material parameters and propagating uncertainty in advanced elastoplastic and damage models, with a focus on multiscale effects and computational efficiency. Deterministic constitutive descriptions based on von Mises plasticity, the Gurson porous plasticity model, and the Lemaitre–Chaboche damage model are embedded into a probabilistic setting in which yield, hardening, damage, and porosity evolution parameters are treated as random variables. Hierarchical priors are introduced to account for microscale variability, enabling consistent uncertainty propagation from material heterogeneity to macroscopic mechanical response. Bayesian inverse problems associated with these models are formulated explicitly through likelihood functions constructed from mechanical data, including cyclic loading histories that give rise to fatigue-like degradation via accumulated plasticity and damage evolution, without introducing an explicit life-based fatigue law. Posterior distributions are approximated using adaptive MCMC and hierarchical VI. To alleviate the computational cost of repeated forward evaluations, neural-network-based surrogate models are employed for likelihood evaluation, enabling efficient posterior sampling and approximation. The proposed framework achieves up to two orders of magnitude reduction in computational time compared to direct finite element simulations while maintaining high predictive accuracy, with surrogate-based inference exhibiting root-mean-square errors below 1%. The results demonstrate improved parameter identifiability, physically consistent uncertainty bounds on stress–strain response and damage evolution, and scalable performance for high-dimensional parameter spaces. Overall, the study establishes a robust and extensible Bayesian framework for uncertainty-aware plasticity and damage modeling, suitable for multiscale analysis and real-time, uncertainty-informed structural assessment.

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