@article{THOMAS2017a,
title = {The exploration of nonlinear elasticity and its efficient parameterization for crystalline materials},
journal = {Journal of the Mechanics and Physics of Solids},
volume = {107},
pages = {76-95},
year = {2017},
issn = {0022-5096},
doi = {https://doi.org/10.1016/j.jmps.2017.06.009},
url = {https://www.sciencedirect.com/science/article/pii/S0022509616309309},
author = {John C. Thomas and Anton {Van der Ven}},
keywords = {Finite strain, Elastic material, Anisotropic material, Constitutive behavior, Numerical algorithms},
abstract = {Conventional approaches to analyzing the very large coherency strains that can occur during solid-state phase transformations are founded in linear elasticity and rely on infinitesimal strain metrics. Despite this, there are many technologically important examples where misfit strains of multi-phase mixtures are very large during their synthesis and/or application. In this paper, we present a framework for constructing strain-energy expressions and stress-strain relationships beyond the linear-elastic limit for crystalline solids. This approach utilizes group theoretical concepts to minimize both the number of free parameters in the strain-energy expression and amount of first-principles training data required to parameterize strain-energy models that are invariant to all crystal symmetries. Within this framework, the strain-energy and elastic stiffness can be described to high accuracy in terms of a set of conventional symmetry-adapted finite strain metrics that we define independent of crystal symmetry. As an illustration, we use first-principles electronic structure data to parameterize strain energy polynomials and employ them to explore the strain-energy surfaces of HCP Zr and Mg, as well as several important Zr-H and Mg-Nd phases that are known to precipitate coherently within the HCP matrices of Zr and Mg.}
}

@article{CASM,
title = {CASM — A software package for first-principles based study of multicomponent crystalline solids},
journal = {Computational Materials Science},
volume = {217},
pages = {111897},
year = {2023},
issn = {0927-0256},
doi = {https://doi.org/10.1016/j.commatsci.2022.111897},
url = {https://www.sciencedirect.com/science/article/pii/S0927025622006085},
author = {Brian Puchala and John C. Thomas and Anirudh Raju Natarajan and Jon Gabriel Goiri and Sesha Sai Behara and Jonas L. Kaufman and Anton {Van der Ven}},
keywords = {Software, Casm, Ab initio, First principles, Open source, Thermodynamics, Kinetics, Alloy, Crystal structure, Symmetry, Crystal structure enumeration, Cluster expansion, Effective Hamiltonian, Monte Carlo, Kinetic Monte Carlo}
}