Knowles, J. K.; Sternberg, Eli Anti-plane shear fields with discontinuous deformation gradients near the tip of a crack in finite elastostatics. (English) Zbl 0503.73078 J. Elasticity 11, 129-164 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 17 Documents MSC: 74R05 Brittle damage 74B20 Nonlinear elasticity Keywords:determining elastostatic field; near tip of crack; all-round infinite body; deformed by Mode III loading at infinity; state of anti-plane shear; class of incompressible, homogeneous, isotropic elastic materials; loss of ellipticity in governing displacement equation of equilibrium; small-scale nonlinear crack problem; crack of finite length replaced by semi-infinite one; nonlinear field far from crack-tip matched to near field; two symmetrically located curves; discontinuities in displacement gradient and stress Citations:Zbl 0432.73088 PDFBibTeX XMLCite \textit{J. K. Knowles} and \textit{E. Sternberg}, J. Elasticity 11, 129--164 (1981; Zbl 0503.73078) Full Text: DOI References: [1] J. K., Knowles and Eli, Sternberg, Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: an example, Journal of Elasticity 10 (1980) 81–110. · Zbl 0432.73088 · doi:10.1007/BF00043136 [2] J. K., Knowles, The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids, International Journal of Fracture, 13, (1977) 611. · doi:10.1007/BF00017296 [3] J. K., Knowles and Eli, Sternberg, On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics, Journal of Elasticity 8 (1978) 329. · Zbl 0422.73038 · doi:10.1007/BF00049187 [4] J. K., Knowles, On the dissipation associated with equilibrium shocks in finite elasticity. Journal of Elasticity 9 (1979) 131. · Zbl 0407.73037 · doi:10.1007/BF00041322 [5] J. R., Rice, Stresses due to a sharp notch in a work-hardening elastic-plastic material loaded by longitudinal shear, Journal of Applied Mechanics 34 (1967) 287. [6] R., Courant and K. O., Friedrichs, Supersonic flow and shock waves, Interscience, New York, 1948. · Zbl 0041.11302 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.