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: Several finite elastic strain measures are evaluated for use in constitutive models of crystalline elasticity and elastoplasticity. 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. Solutions to the planar shock problem from previous work are summarized, and new applications of logarithmic strain-based theory toward shock compression of aluminum, copper, and magnesium single crystals and polycrystals are presented. Consideration of these new results in conjunction with previous analysis for metals, ceramics, and minerals suggests that Eulerian strain-based theory is preferred for typical ductile metallic crystals, while logarithmic strain-based theory is recommended for modeling shocks in ceramics and minerals with larger ratios of shear modulus to bulk modulus.

Reformulation of Nonlinear Anisotropic Crystal Elastoplasticity for Impact Physics