LINEAR AND NONLINEAR SCATTERING OF ELASTIC-WAVES BY MICROCRACKS

PROBLEMS OF ELASTODYNAMIC scattering by a penny-shaped microcrack whos e response may be either linear or nonlinear are studied. Linear scatt ering results from the assumption that either the crack faces never co me into contact. or, alteratively, they remain in permanent gliding co ntact. Nonlinearity arises when a unilateral constraint is introduced. corresponding to opening of the crack during tension and closure duri ng compression. Attention is focused on low frequency asymptotic behav iour of the scattering cross-section Q for time-periodic solutions. Th e quasistatic approximation for the jump of the displacement vector ac ross the crack is the key tool for construction of the asymptotics of Q at low frequencies. Explicit formulate are given for different types of cracks. The results differ essentially, both quantitatively and qu alitatively, for linear and nonlinear scatterers. Among the latter, cl osing cracks with and without sliding friction are considered. The mai n contribution is delivered in these cases by shock waves radiated at moments of opening and closure. Numerical results based on the explici t formulae are presented.