Finite deformation of a blunt crack represented by a parabolic cavity in a harmonic solid

Abstract

We study the finite plane deformation of a blunt crack represented by a parabolic cavity in a particular class of compressible hyperelastic materials of harmonic type. A complete solution to the blunt crack problem is derived using complex variable techniques. Elementary expressions of the stresses along the real axis ahead of the vertex of the parabola and the finite deformation of the parabola are obtained. When the nominal stress intensity factors approach zero, the stress distributions along the real axis are identical to those in linear elasticity. When the nominal stress intensity factors approach infinity, the tractions along the real axis are inversely proportional to the square root of the horizontal coordinate. A finite and non-zero mode II nominal stress intensity factor will induce both shear and normal stresses along the real axis, a phenomenon quite different from that for linear elasticity.