Accession Number : ADA119029

Title :   Finite Plane and Anti-Plane Elastostatic Fields with Discontinuous Deformation Gradients Near the Tip of a Crack.

Descriptive Note : Technical rept.,

Corporate Author : CALIFORNIA INST OF TECH PASADENA DIV OF ENGINEERING AND APPLIED SCIENCE

Personal Author(s) : Fowler,Graeme Francis

PDF Url : ADA119029

Report Date : Jul 1982

Pagination or Media Count : 88

Abstract : In this paper the fully nonlinear theory of finite deformations of an elastic solid is used to study the elastostatic field near the tip of a crack. The special elastic materials considered are such that the differential equations governing the equilibrium fields may lose ellipticity in the presence of sufficiently severe strains. The first problem considered involves finite anti-plane shear (Mode III) deformations of a cracked incompressible solid. The analysis is based on a direct asymptotic method, in contrast to earlier approaches which have depended on hodograph procedures. The second problem treated is that of plane strain of a compressible solid containing a crack under tensile (Mode I) loading conditions. The material is characterized by the so-called Blatz-Ko elastic potential. Again, the analysis involves only direct local considerations. For both the Mode III and Mode I problems, the loss of equilibrium ellipticity results in the appearance of curves ('elastostatic shocks') issuing from the crack-tip across which displacement gradients and stresses are discontinuous. (Author)

Descriptors :   *Mathematical analysis, *Nonlinear differential equations, *Cracks, *Crack propagation, Elastic properties, Plastic deformation, Strain(Mechanics), Stresses, Compressible flow, Rubber, Shear properties, Displacement, Gradients, Flow fields, Equilibrium(General), Finite difference theory, Applied mathematics

Subject Categories : Physical Chemistry
      Numerical Mathematics
      Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE