The exploration of nonlinear elasticity and its efficient parameterization for crystalline materials

• Published in: Journal of the mechanics and physics of solids Vol. 107; no. C; pp. 76 - 95
• Main Authors: Thomas, John C., Van der Ven, Anton
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.10.2017; Elsevier BV; Elsevier
• Subjects: Algorithms; Anisotropic material; Constitutive behavior; Crystal structure; Crystallization; Crystals; Elastic limit; Elastic material; Elasticity; Electronic structure; Energy conservation; Finite strain; MATERIALS SCIENCE; Numerical algorithms; Parameterization; Phase transitions; Stiffness; Strain; Stress-strain relationships; Symmetry; Zirconium; Anisotropic material; Elastic material; Constitutive behavior; Finite strain; Numerical algorithms
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2017.06.009

•Identify universal set of symmetry-adapted strain order parameters for crystalline materials.•Present computational framework to construct nonlinear elastic energy models for crystalline materials.•Describe group-theoretical algorithms for exploring and analyzing nonlinear elasticity.•Apply methods to example cases of Mg-Nd alloy phase and Zr-hydride phases. 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.