Determination of the near-tip stress fields for the scattering of P-waves by a crack. (English) Zbl 0732.73015
Summary: A conservation law implied by the field equations of linear elastodynamics is derived, and a procedure based on this conservation law is given for the direct determination of the near-tip stress fields arising from the scattering of normally incident P-waves by a crack in a homogeneous, isotropic elastic medium.
MSC:
| 74J20 | Wave scattering in solid mechanics |
| 74G70 | Stress concentrations, singularities in solid mechanics |
| 74R99 | Fracture and damage |
Keywords:
transient scattering; plane strain longitudinal wave; semi-infinite crack; linear elastodynamics; normally incident P-waves; homogeneous, isotropic elastic mediumReferences:
| [1] | Jiang, Q., Knowles, J. K.: On the direct determination of the near-tip stress field for the scattering of SH-waves by a crack. Int. J. Fract.41, 283-288 (1989). · doi:10.1007/BF00018860 |
| [2] | DeHoop, A. T.: Representation theorems for the displacement in an elastic solid and their application to elastodynamic diffraction theory. Doctoral Dissertation, Technische Hogeshool, Delft, The Netherlands (1958). |
| [3] | Freund, L. B.: Dynamic fracture mechanics, pp. 72-97. Cambridge: Cambridge University Press 1990. · Zbl 0712.73072 |
| [4] | Gurtin, M. E.: Variational principles for linear initial value problems. Quart. Appl. Math.22, 252-256 (1964). · Zbl 0173.37602 |
| [5] | Knowles, J. K., Sternberg, E.: On a class of conservation laws in linearized and finite elastostatics. Arch. Rat. Mech. Anal.44, 187-211 (1972). · Zbl 0232.73017 · doi:10.1007/BF00250778 |
| [6] | Jiang, Q.: On conservation laws in viscoelastostatics. Acta Mechanica56, 219-227 (1985). · Zbl 0581.73042 · doi:10.1007/BF01177119 |
| [7] | Jiang, Q.: Conservation laws of linear viscoelastodynamics. J. Elasticity16, 213-219 (1986). · Zbl 0585.73019 · doi:10.1007/BF00043587 |
| [8] | Caviglia, G., Morro, A.: A general approach to conservation laws in viscoelasticity. Acta Mechanica75, 255-267 (1988). · Zbl 0667.73029 · doi:10.1007/BF01174639 |
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