Some dynamical problems in non classical theory of elasticity

Abstract

The theories of elastic-plastic material with voids and the nonlocal micropolar thermoelastic material with voids have been developed. The constitutive relations and equations of motion for different anisotropy and isotropic elastic-plastic material with voids have been derived. The effect of plasticity is considered through a single slip-plane and direction. The dispersion relation for uni-directional wave propagation in the anisotropic as well as isotropic elastic-plastic material with voids is obtained. The possibility of propagation of Lamb waves in an elastic-plastic plate containing a uniform distribution of voids has been explored. The frequency equations corresponding to the symmetric and anti-symmetric families of Lamb modes are derived. The constitutive relations and equations of motion are derived for the nonlocal micropolar thermoelastic material with voids. The dispersion relation for plane wave s propagation in the nonlocal micropolar thermoelastic material with voids is obtained. The reflection phenomenon of coupled waves through a boundary surface of a nonlocal micropolar thermoelastic half-space containing voids has been studied. The reflection coefficients and the corresponding energy ratios are derived by assuming the boundary of the half-space is mechanically stress-free and thermally insulated. newline