A model for finite-deformation nonlinear thermomechanical response of single crystal copper under shock conditions

• Published in: Journal of the mechanics and physics of solids 2013-09, Vol.61 (9), p.1877-1894
• Main Authors: Luscher, Darby J., Bronkhorst, Curt A., Alleman, Coleman N., Addessio, Francis L.
• Format: Article
• Language: English
• Subjects: BICRYSTALS; Copper; Crystal anisotropy; Crystals; Decomposition; DEFORMATION; Elastic deformation; ELASTIC STRAIN; Equation of state; Internal state variable; MATHEMATICAL ANALYSIS; Shock loading; SINGLE CRYSTALS; STRAIN; Symmetry; THERMOMECHANICAL TREATMENTS
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2013.05.002

A physically consistent framework for combining pressure–volume–temperature equations of state with crystal plasticity models is developed for the application of modeling the response of single and polycrystals under shock conditions. The particular model is developed for copper, thus the approach focuses on crystals of cubic symmetry although many of the concepts in the approach are applicable to crystals of lower symmetry. We employ a multiplicative decomposition of the deformation gradient into isochoric elastic, thermoelastic dilation, and plastic parts leading to a definition of isochoric elastic Green-Lagrange strain. This finite deformation kinematic decomposition enables a decomposition of Helmholtz free-energy into terms reflecting dilatational thermoelasticity, strain energy due to long-range isochoric elastic deformation of the lattice and a term reflecting energy stored in short range elastic lattice deformation due to evolving defect structures. A model for the single crystal response of copper is implemented consistent with the framework into a three-dimensional Lagrangian finite element code. Simulations exhibit favorable agreement with single and bicrystal experimental data for shock pressures ranging from 3 to 110GPa. •We develop a physically consistent framework for modeling single crystal nonlinear elasticity and plasticity.•Physical inconsistencies of some previous approaches in decomposing elastic strain are detailed.•A new isochoric elastic Green-Lagrange strain is defined to decouple volumetric and deviatoric response.•The framework is applied to modeling shock response of copper single- and bi-crystals.•Example simulations exhibit favorable agreement to published experimental results.