System identification and reliability assessment of hyperelastic materials via an efficient sparsity-promoting variational Bayesian approach

Abstract

In this study, an efficient data-driven approach to identify constitutive models for isotropic hyperelastic materials is introduced, which is crucial for predicting material behavior and subsequently evaluating its reliability. This innovative method allows for reliability assessment, even when the precise material model is unknown beforehand. First, a data-driven physics-preserving approach for identifying constitutive models that describe the stress–strain relationships of isotropic hyperelastic materials is developed. A manually designed library of polynomial basis functions inspired by existing models for rubber-like materials is utilized. To achieve a sparse selection of features from this library, a Bayesian sparse regression technique is employed, implementing a sparsity-promoting spike-and-slab prior. Instead of using the computationally intensive Markov Chain Monte Carlo (MCMC) method for Bayesian posterior inference, a more efficient Variational Bayesian (VB) approach is opted for, significantly reducing computational time. The effectiveness of the constitutive model identification procedure is demonstrated through various numerical examples. Next, attention is turned to the estimation of reliability for hyperelastic materials under parametric uncertainty. Given that the constitutive model is unknown beforehand, multiple specimens of the material are utilized to determine a common underlying model and identify parameter distributions. These parameter distributions are then employed to estimate the Probability of Failure (PF) through Monte Carlo simulations. The results showcase the versatility of the proposed approach, not only in predicting material behavior and calibrating models but also in calculating the PF for hyperelastic materials, even in situations where the underlying model is not known in advance.