Predicting ductile fracture of engineering structures under complex loading environments is a well-known challenge in engineering mechanics. One popular approach is to apply continuum damage models that record damage using internal state variables to represent the micromechanics at play. The most heavily used models are dated phenomenological models derived with a set of simplifying assumptions that constrain the micromechanics to a non-physical domain. Common assumptions include self-similar void growth, isotropic matrix material, and the use of plastic limit theory. Nevertheless, these models have proven very effective and are rooted in interpretability afforded by relatively simple equation forms that summarize their physics-based foundation. Our work explores the relaxation of these simplifying assumptions by leveraging modern computing capabilities and machine learning.Among other benefits, interpretability allows for engineering intuition and clear behavior at the bounds. Maintaining interpretability using modern data-driven techniques is possible through symbolic regression, a machine learning method that targets accuracy and simplicity in searching for mathematical expressions to fit a dataset. The resulting damage models remain compatible with existing computational mechanics frameworks. A common technique used in symbolic regression is genetic programming, which draws inspiration from the theory of natural evolution in biology. In the current study, the open-source software Bingo is used to demonstrate the effectiveness of using genetic programming with symbolic regression (GPSR) in the development of interpretable material damage models in engineering alloys.In recently published work, GPSR was shown to be capable of learning, in symbolic form, von Mises plasticity with state variable evolution [Bomarito et al., C&amp;S 2021]. The current study extends this to using GPSR within the context of existing damage models, specifically those involved with the fracture of porous, ductile metals. In particular, the current work is focused on the Gurson model, which accounts for the coupling between plastic material response and damage evolution in porous metals [Gurson, J Eng Mater Technol 1977]. Training data are generated using numerical integration of the Gurson elastoplastic model with realistic material properties and loading scenarios. Preliminary results have shown that GPSR is able to symbolically produce the Gurson model given these training data. Ongoing studies into the optimal dataset size and GPSR hyperparameters will further improve the framework being used in the development of interpretable damage models using GPSR. Additionally, we are working to enforce mechanics-based concepts in the GPSR evolutionary process by penalizing physically unrealistic constitutive models using a priori knowledge to promote validity of the produced models.Further related work is focused on relaxing simplifying assumptions in the Gurson model while retaining interpretability in the resulting GPSR models. Training data are generated using finite element simulations of microstructures representative of porous, ductile metals. Simplifying assumptions in the Gurson model, such as a symmetric array of voids and self-similar void growth, are then systematically relaxed in the finite element models, with differences in the GPSR models attributed to their respective assumptions being relaxed.(Sandia National Laboratories is managed and operated by NTESS under DOE NNSA contract DE-NA0003525)

Physics-Informed Machine Learning for the Development of Microstructure-Sensitive Deformation and Damage Models in Engineering Applications

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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