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Understanding material failure is critical for designing stronger and lighter structures by identifying weaknesses that could be mitigated. Existing full-physics numerical simulation techniques involve trade-offs between speed, accuracy, and the ability to handle complex features like varying boundary conditions, grid types, resolution, and physical models. We present the first foundation model specifically designed for predicting material failure, leveraging large-scale datasets and a high parameter count (up to 3B) to significantly improve the accuracy of failure predictions. In addition, a large language model provides rich context embeddings, enabling our model to make predictions across a diverse range of conditions. Unlike traditional machine learning models, which are often tailored to specific systems or limited to narrow simulation conditions, our foundation model is designed to generalize across different materials and simulators. This flexibility enables the model to handle a range of material properties and conditions, providing accurate predictions without the need for retraining or adjustments for each specific case. Our model is capable of accommodating diverse input formats, such as images and varying simulation conditions, and producing a range of outputs, from simulation results to effective properties. It supports both Cartesian and unstructured grids, with design choices that allow for seamless updates and extensions as new data and requirements emerge. Our results show that increasing the scale of the model leads to significant performance gains (loss scales as $N^{-1.6}$, compared to language models which often scale as $N^{-0.5}$)., Comment: Accepted at NeurIPS 2024 "Foundation Models for Science: Progress, Opportunities, and Challenges" Workshop

In this work, we apply a phase-field modeling framework to elucidate the interplay between nucleation and kinetics in the dynamic evolution of twinning interfaces. The key feature of this phase-field approach is the ability to transparently and explicitly specify nucleation and kinetic behavior in the model, in contrast to other regularized interface models. We use this to study 2 distinct problems where it is essential to explicitly specify the kinetic and nucleation behavior governing twin evolution. First, we study twinning interfaces in 2-d. When these interfaces are driven to move, we find that significant levels of twin nucleation occur ahead of the moving interface. Essentially, the finite interface velocity and the relaxation time of the stresses ahead of the interface allows for nucleation to occur before the interface is able to propagate to that point. Second, we study the growth of needle twins in antiplane elasticity. We show that both nucleation and anisotropic kinetics are essential to obtain predictions of needle twins. While standard regularized interface approaches do not permit the transparent specification of anisotropic kinetics, this is readily possible with the phase-field approach that we have used here., Comment: To appear in Journal of Applied Mechanics

We briefly compare the structure of two classes of popular models used to describe poro- and chemo- mechanics wherein a fluid phase is transported within a solid phase. The multiplicative deformation decomposition has been successfully used to model permanent inelastic shape change in plasticity, solid-solid phase transformation, and thermal expansion, which has motivated its application to poro- and chemo- mechanics. However, the energetic decomposition provides a more transparent structure and advantages, such as to couple to phase-field fracture, for models of poro- and chemo- mechanics.

This work begins by applying peridynamics and phase-field modeling to predict 1-d interface motion with inertia in an elastic solid with a non-monotone stress-strain response. In classical nonlinear elasticity, it is known that subsonic interfaces require a kinetic law, in addition to momentum balance, to obtain unique solutions; in contrast, for supersonic interfaces, momentum balance alone is sufficient to provide unique solutions. This work finds that peridynamics agrees with this classical result, in that different choices of regularization parameters provide different kinetics for subsonic motion but the same kinetics for supersonic motion. In contrast, conventional phase-field models coupled to elastodynamics are unable to model, even qualitatively, the supersonic motion of interfaces. This work identifies the shortcomings in the physics of standard phase-field models to be: (1) the absence of higher-order stress to balance unphysical stress singularities, and (2) the ability of the model to access unphysical regions of the energy landscape. Based on these observations, this work proposes an augmented phase-field model to introduce the missing physics. The augmented model adds: (1) a viscous stress to the momentum balance, in addition to the dissipative phase-field evolution, to regularize singularities; and (2) an augmented driving force that models the physical mechanism that keeps the system out of unphysical regions of the energy landscape. When coupled to elastodynamics, the augmented model correctly describes both subsonic and supersonic interface motion. The augmented model has essentially the same computational expense as conventional phase-field models and requires only minor modifications of numerical methods, and is therefore proposed as a replacement to the conventional phase-field models.