Abstract
Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.
Highlights
Nonlinear, anisotropic elastic properties of single crystals determine material response to extreme loading, e.g., in shock waves, under high static pressure, and in defect-free crystals and nanoregions
Stress–strain curves at finite strains are obtained[4,5,10,18,19,29,30,31], yet this is insufficient for simulation of material behavior or describing lattice instabilities under arbitrary complex loadings
Motion of an elastic body is described by vector function xi(Xj, t), where t is time and xi and Xj are the Cartesian coordinates of the position vector in a natural cubic coordinate system
Summary
Anisotropic elastic properties of single crystals determine material response to extreme loading, e.g., in shock waves, under high static pressure, and in defect-free crystals and nanoregions. C44456 η4 η5 η6 ðη[24] þ η25 þ η26Þþ c12244 1⁄2η1 ðη[22] þ η23 Þη24 þ η2ðη[21] þ η23Þη25 þ η3ðη[21] þ η22Þη26þ c11244 1⁄2η21 ðη[2] þ η3Þη24 þ η22ðη[1] þ η3Þη25 þ η23ðη[2] þ η1Þη26: phases, under pressure or normal stresses, much lower than traditionally accepted 10–12 GPa. conditions for semiconductor-metal transitions under complex triaxial loading were determined by DFT simulations in ref.
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