An infinitely long cylindrical cavity in an infinite elastic homogeneous and isotropic medium is enveloped by a plane shock wave whose front is parallel to the axis of the cavity. An integral transform technique is used to determine the stress field produced in the medium by the diffraction of the incoming shock wave by the cavity. Expressions for the radial stress σrr, the hoop stress σθθ, and the shear stress σrθ are derived as inversion integrals, and numerical results are presented for the time-history of the hoop stress σθθ at the boundary of the cavity. The amplifications of the hoop-stress concentration factors due to the dynamic loading are noted. The problem is considered for pressure waves with a step distribution in time. These results may be used as influence coefficients to determine, by means of Duhamel integrals, the stress field produced by waves with time-varying pressures.
Nondimensional stress variable. 1 I + a2 y Angle between a 1 and position ray of element, Fig. 4. 8 Angle between a and normal to S-front. a 0-3 Small quantity for purposes of asymptotic expansion. Poisson's ratio. t-3.14159... p Wasi density of medium. "ij ,Stresses, stress rates. Ol ' 03 Principal stresses. Shear stress. CP Position angle of element, Fig. 4. VP CP S) Position of elastic P-and Sand inelastic shock fronts, respectively. 'P1 'V2 Limits of inelastic region. # Angle of internal friction. Differentiation with respect to c. ix '1 1~2 2 1 cos 0 sin (cp-)s I + sin 9 cos (pa' s + sin cp J 2 9
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.