Stochastic Modeling of Anisotropic Strength Surfaces from Atomistic Simulations

Abstract

This work develops a unified framework for inferring, representing, and statistically characterizing an anisotropic strength surface directly from molecular dynamics data. Large-scale tensile loading simulations are used to generate failure data across all principal stress ratios and loading orientations, facilitated by a data-driven mapping between imposed strain-rate tensors and resulting stresses. The orientation-dependent strength surface is then represented using a constrained parametric formulation in which the surface parameters vary smoothly with loading angle through a low-dimensional functional encoding. To deploy the framework, we specifically consider the case of monocrystalline graphene, which is a prototypical two-dimensional material that has been extensively characterized, both experimentally and computationally, in the literature. For defective graphene, multiple random realizations of vacancy defect distributions are used to construct a stochastic ensemble of angular strength surfaces. Because each anisotropic strength surface requires substantial atomistic sampling to construct, the resulting ensemble is inherently limited in size, motivating the use of compact encoding, dimensionality reduction, and probabilistic modeling to characterize strength variability. Dimensionality reduction via Principal Component Analysis reveals a condensed latent representation of the fitted, encoded surfaces, where a Gaussian mixture model is employed to capture defect-induced variability, including rare outlier behaviors arising from clustered vacancy defects. Sampling from this probabilistic model enables the generation of new, physically admissible strength surfaces and the construction of confidence intervals in both parameter space and stress space. (Abstract shortened to meet arXiv limits.)