Discontinuous Deformation Gradients Near the Tip of a Crack in Finite Anti-Plane Shear: An Example.
CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE
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This investigation aims at the elastostatic field near the edges tips of a plane crack of finite width in an all-around infinite body, which - at infinity - is subjected to a state of simple shear parallel to the crack faces. The analysis is carried out within the fully nonlinear equilibrium theory of homogeneous and isotropic, incompressible elastic solids. Further, the particular constitutive law employed here gives rise to a loss of ellipticity of the governing displacement equation of equilibrium in the presence of sufficiently severe anti-plane shear deformations. The study reported in this paper is asymptotic in the sense that the actual crack is replaced by a semi-infinite one, while the far field is required to match the elastic field predicted near the crack tips by the linearized theory for a crack of finite width. The ensuing global boundary-value problem thus characterizes the local state of affairs in the vicinity of a crack-tip, provided the amount of shear applied at infinity is suitably small.
- Theoretical Mathematics