Linear and nonlinear scattering of elastic waves by microcracks

• Published in: Journal of the mechanics and physics of solids Vol. 42; no. 4; pp. 585 - 610
• Main Authors: Smyshlyaev, V.P., Willis, J.R.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.04.1994; Elsevier
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Microcracks; Crack closure effect; Elastic waves; Low frequency; Cross sections; Sliding friction; Scattering theory
• ISSN: 0022-5096
• DOI: 10.1016/0022-5096(94)90053-1

Problems of elastodynamic scattering by a penny-shaped microcrack whose response may be either linear or nonlinear are studied. Linear scattering results from the assumption that either the crack faces never come into contact, or, alternatively, they remain in permanent gliding contact. Nonlinearity arises when a unilateral constraint is introduced, corresponding to opening of the crack during tension and closure during compression. Attention is focused on low frequency asymptotic behaviour of the scattering cross-section Q for time-periodic solutions. The quasistatic approximation for the jump of the displacement vector across the crack is the key tool for construction of the asymptotics of Q at low frequencies. Explicit formulae are given for different types of cracks. The results differ essentially, both quantitatively and qualitatively, for linear and nonlinear scattcrers. Among the latter, closing cracks with and without sliding friction are considered. The main contribution is delivered in these cases by shock waves radiated at moments of opening and closure. Numerical results based on the explicit formulae are presented.