Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with orthorhombic symmetry

Abstract

Articles you may be interested inElastic properties of polycrystals with trigonal crystal and orthorhombic specimen symmetry J. Appl. Phys. 60, 3868 (1986); 10.1063/1.337558Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with trigonal (3,3) and tetragonal (4,4,4m) symmetry Bounds on the effective elastic moduli of randomly oriented aggregates of orthorhombic crystals have been derived using the variational principles of Hashin and Shtrikman. The bounds are considerably narrower than the widely used Voigt bound and Reuss bound. In many instances, the separation between the new bounds is comparable to, or less than, the uncertainty introduced by experimental errors in the single-crystal elastic stiffnesses. The Voigt-Reuss-Hill average lies within the Hashin-Shtrikman bounds.

Random polycrystals of grains containing cracks: Model of quasistatic elastic behavior for fractured systems

“…K V RH and G V RH can both be computed easily for these stiffnesses using the formulas given by Watt [16] for orthorhomic symmetry. But, after the averaged matrices C SM P ij were computed as in (1), these matrices were slightly "smoothed" (in addition to the averaging) so the results had exactly hexagonal symmetry.…”

“…Then, a similar calculation was done for the shear modulus G V RH . Formulas for all these averages are given for orthotropic elastic stiffness matrices by Watt [16]. The results (VRH) are plotted as red ×'s in Figures 2-9, where the numerical results are also compared to results from the differential scheme (DS), the non-interacting approximation (NI), and various bounds and estimates based on random polycrystals of cracked grains (R,HS − ,SC,HS + ,V).…”

Combining analysis of random elastic polycrystals with poroelasticity for granular composites having orthotropic porous grains and fluid-filled pores

“…Results of Watt [22] for bounds on bulk modulus bounds K ± HS and those of Middya and Basu [23] for self-consistent estimates K * SC of bulk modulus can both be written in virtually the same form:…”

“…This work will be only briefly elaborated. In particular, a useful "shooting method of optimization" (which makes use of the computed values of the selfconsistent estimates in order to speed up the search for HS bounds) was developed previously to streamline the algorithm used to produce the Hashin-Shtrikman bounds [11,13,14,22].…”

Evaluating bounds and estimators for constants of random polycrystals composed of orthotropic elastic materials

“…Results of Watt [15] for bounds on bulk modulus K ± HS and those of Middya and Basu [16] for self-consistent estimates K * SC of bulk modulus can both be written in virtually the same form:…”