Formulas for the pressure and bulk modulus in uniaxial strain

摘要: For an isotropic elastic solid, the pressure p=pu(ρ) in a state of uniaxial strain at density ρ generally differs from p=ph(ρ) hydrostatic stress same density. Several researchers have used pressure/shear (or oblique plate impact) tests to determine pu and corresponding bulk modulus Ku≡ρdpu/dρ. The yield longitudinal shear moduli, Lu Gu, as function ρ. A common procedure is integrate approximate relation Ku≈Lu−43Gu obtain pressure-density strain. It shown here that integration this between moduli can be avoided altogether by utilizing exact formula pu=σ1−23((ρ/ρ0)2−1)Gu, where σ1 denotes (pos. compression). Ku computed exactly formula, error approximating it Lu−43Gu determined.