Physics-Based and Data-Driven Computational Models of Inelastic Deformations

Citation

Ocegueda, Eric (2023) Physics-Based and Data-Driven Computational Models of Inelastic Deformations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3gqd-zp93. https://resolver.caltech.edu/CaltechTHESIS:05312023-212652388

Abstract

Crystalline materials inevitably exhibit inelastic deformation when applied to large enough loads. The behavior in this inelastic regime is a coupling of physics across several length scales: from initiating as defects at the atomic scale, interacting with crystal defects, and finally spanning multiple grains and influencing macroscopic stress behavior. These length-scale interactions make predicting material response an open challenge and an avenue for leveraging microscale physics for material design. This thesis examines developing physics-based and data-driven computational models to capture complex inelastic behavior at appropriate length scales.

First, we present a mesoscale model for capturing deformation twinning physics at the polycrystal scale. Mechanical twinning is a form of inelastic deformation observed in low-symmetry crystals, such as magnesium and other hexagonal close-packed (hcp) metals. Twinning, unlike slip, forms as bands collectively across grains with complex local morphology propagating into bulk behavior, drastically affecting strength and ductility. We, thus, propose a model where twinning is treated using a phase-field approach, while dislocation slip is considered using crystal plasticity. Lattice reorientation, length-scale effects, interactions between dislocations and twin boundaries, and twin and slip interactions with grain boundaries are all carefully considered. We first outline the model and its implementation using a novel approach of accelerated computational micromechanics in a two-dimensional, single twin-slip system, polycrystal case to demonstrate its capabilities. Finally, we consider multiple twin-slip systems and conduct three-dimensional simulations of polycrystalline magnesium. We summarize the insights gained from these studies and the implications on the macroscale behavior of hcp materials.

The second part of the thesis focuses on data-driven models for capturing microscopic history-dependent phenomena for multiscale modeling applications. The multiscale modeling framework has seen increased usage over the last few decades for its ability to capture complex material behavior over a range of time/length scales by solving a macroscale problem directly with a constitutive relation defined implicitly by the solution of a microscale problem. However, this implementation is computationally expensive -- needing to solve a microscale problem at each point and time of the macroscopic calculation. In this study, we examine the use of machine learning by utilizing data generated through repeated solutions of a microscale problem to: (i) gain insights into the history dependent macroscopic internal variables that govern the response and (ii) create a computationally efficient surrogate. We do so by introducing a recurrent neural operator, which can provide accurate approximations of the stress response and insights into the physics of the macroscopic problem. We illustrate these capabilities on a laminate composite and polycrystal made of elasto-viscoplastic materials, summarize insights on the learned internal variables, and accuracy of stress predictions.

Thesis Files