GENERAL-SOLUTION AND GREEN-FUNCTION WITH BIFURCATION FOR NONLINEAR PLANE-STRESS DEFORMATION OF A COMPRESSIBLE WEDGE

Exact stress, strain and displacement fields with closed form are dete rmined for a nonlinear boundary value wedge problem. The compressible wedge experiencing small plane stress deformation is loaded by a conce ntrated force at its apex and the material is assumed to satisfy the p ower-law sigma(E) = E(0) epsilon(E)(n) where E(0) and n (0 < n less th an or equal to 1) are positive constants, sigma(E) and epsilon(E) are the stress and strain intensities, respectively. The results show that bifurcation with three branches occurs when the value of n is close t o v/(1+v) where v is the Poisson ratio. The discontinuity of displacem ent components and their gradients proves to exist if the solution per taining to one branch characterized by n = v/(1 + v) is required to sa tisfy the symmetric and theta-dependence conditions. These phenomena c an be ascribed to the property conversion of the governing equation fr om the elliptic (n > v/(1 + v)) to parabolic (n = v/(1 + v)) or hyperb olic type (n < v/(1 + v)). As illustrative examples, the Green functio ns are ascertained for a half plane subjected to a normal and a shear forces, respectively. It is found that the stress distribution for sym metric problems of the three branches fundamentally differs from each other. For deformation of the elliptic type, two fanlike tensile zones are discovered near the boundary of the half plane loaded by a compre ssive normal force. Copyright (C) 1996 Elsevier Science Ltd.