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- W4200475973 abstract "A general nonlinear theory for the elasticity of prestressed single crystals is presented. Various types of elastic moduli are defined, their importance is determined, and relationships between them are presented. In particular, $mathbit{B}$ moduli are present in the relationship between the Jaumann objective time derivative of the Cauchy stress and deformation rate and are broadly used in computational algorithms in various finite-element codes. Possible applications to simplified linear solutions for complex nonlinear elasticity problems are outlined and illustrated for a superdislocation. The effect of finite rotations is fully taken into account and analyzed. Different types of the bulk and shear moduli under different constraints are defined and connected to the effective properties of polycrystalline aggregates. Expressions for elastic energy and stress-strain relationships for small distortions with respect to a prestressed configuration are derived in detail. Under initial hydrostatic load, general consistency conditions for elastic moduli and compliances are derived that follow from the existence of the generalized tensorial equation of state under hydrostatic loading obtained from a single crystal or polycrystal. It is shown that $mathbit{B}$ moduli can be found from the expression for the Gibbs energy. However, higher order elastic moduli defined from the Gibbs energy do not have any meaning since they do not directly participate in any known equations, like the stress-strain relationships and wave propagation equation. The deviatoric projection of $mathbit{B}$ can also be found from the expression for the elastic energy for isochoric small strain increments, and the missing components of $mathbit{B}$ can be found from the consistency conditions." @default.
- W4200475973 created "2021-12-31" @default.
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- W4200475973 date "2021-12-17" @default.
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- W4200475973 title "Nonlinear elasticity of prestressed single crystals at high pressure and various elastic moduli" @default.
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- W4200475973 doi "https://doi.org/10.1103/physrevb.104.214105" @default.
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