Formulas for the pressure and bulk modulus in uniaxial strain
Abstract
For an isotropic elastic solid, the pressure p=pu(ρ) in a state of uniaxial strain at density ρ generally differs from the pressure p=ph(ρ) in a state of hydrostatic stress at the same density. Several researchers have used pressure/shear (or oblique plate impact) tests to determine pu and the corresponding uniaxial bulk modulus Ku≡ρdpu/dρ. The pressure/shear tests yield uniaxial longitudinal and shear moduli, Lu and Gu, as a function ρ. A common procedure is to integrate the approximate relation Ku≈Lu-4/3Gu to obtain the pressure-density relation p=pu(ρ) in uniaxial strain. It is shown here that the integration of this approximate relation between the moduli can be avoided altogether by utilizing the exact formula pu=σ1-2/3((ρ/ρ0)2-1)Gu, where σ1 denotes the longitudinal stress (pos. in compression). The bulk modulus Ku is computed exactly from this formula, and the error in approximating it by Lu-4/3Gu is determined.
- Publication:
-
Proceedings of the Conference of the American Physical Society topical group on shock compression of condensed matter
- Pub Date:
- May 1996
- DOI:
- 10.1063/1.50681
- Bibcode:
- 1996AIPC..370..475S
- Keywords:
-
- 62.20.Dc;
- 62.20.Fe;
- 62.30.+d;
- 46.30.-i;
- Elasticity elastic constants;
- Deformation and plasticity;
- Mechanical and elastic waves;
- vibrations