Crystal thermoelasticity at extreme loading rates and pressures: Analysis of higher-order energy potentials

Several finite elastic strain measures are evaluated for use in constitutive models of crystalline elasticity and elasto-plasticity. These include the Green material strain tensor, the Eulerian material strain tensor, and the logarithmic material strain tensor, all of which are referred to locally relaxed coordinates invariant under spatial rotations. New applications of logarithmic strain-based theory towards shock compression of aluminum, copper, and magnesium single crystals and polycrystals are presented. Solutions to the planar shock problem from previous work are summarized and compared with the present results. Consideration of these new results in conjunction with previous analysis for a number of different metals, ceramics, and minerals suggests that Eulerian strain-based theory is most accurate for modeling the dynamic high-pressure response of ductile metallic crystals wherein ratios of elastic shear to bulk moduli tend to be relatively small, while logarithmic strain-based theory is recommended for modeling shocks in ceramics and minerals with larger ratios of effective elastic shear to bulk modulus.