COMPLAS 2025

Bayesian parameter identification of nonlinear constitutive laws with strain localization

  • Jafari, Abbas (BAM)
  • Chatzi, Eleni (ETH Zürich)
  • Unger, Jörg F (BAM)

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Mechanical structures are frequently simulated by numerical models developed on the basis of physical laws. Such simulations are significantly influenced by the incorporated material models, which often suffer from considerable uncertainty. These uncertainties are, in general, derived from inadequate physical laws, unrealistic assumptions, and imprecise simplifications. Bayesian techniques are often employed to resolve such uncertainties based on experimental data, particularly those related to model parameters and measurement inaccuracies. This work focuses on the Bayesian parameter identification of a parameterized physics-based constitutive law that is used to describe strain localization. The proposed inference scheme relies on the use of measured integrated forces and full-field displacements. The former essentially are aggregated external forces measured at structural level over certain sub-boundaries. The full field displacements are assumed to be obtained from monitoring procedures, such as Digital Image Correlation (DIC), which are able to return dense observations. As a central idea of the proposed framework, strain localization effects are directly incorporated into the model by introducing Dirichlet constraints from full-field displacements. The objective function to be minimized is then a metric of the discrepancy between the model’s internal forces and the measured aggregated forces. Based on this objective function, a Bayesian inverse problem is formulated and solved using a variational Bayesian method, originally proposed in [1]. The inference scheme further addresses the uncertainty of measured displacements applied as Dirichlet constraints. We verify the proposed framework on two virtual examples, utilizing a gradient damage constitutive law that accounts for strain localization. Further details of the methods and the examples can be found in [2]. REFERENCES: [1] Michael A Chappell et al., Variational Bayesian inference for a nonlinear forward model. In: IEEE Transactions on Signal Processing 57.1 (2008), pp. 223–236. [2] Jafari, Abbas, et al. A Bayesian framework for constitutive model identification via use of full field measurements, with application to heterogeneous materials. In: Computer Methods in Applied Mechanics and Engineering 433 (2025): 117489.