Abstract :
Exact stress, strain and displacement fields with closed form are determined for a
nonlinear boundary value wedge problem. The compressible wedge experiencing small plane stress
deformation is loaded by a concentrated force at its apex and the material is assumed to satisfy the
power-law a~ = E06 where E0 and n (0 < n ~< 1) are positive constants, aE and EE are the stress and
strain intensities, respectively. The results show that bifurcation with three branches occurs when
the value of n is close to v/(1 +v) where v is the Poisson ratio. The discontinuity of displacement
components and their gradients proves to exist if the solution pertaining to one branch characterized
by n = v/(1 + v) is required to satisfy the symmetric and 0-dependence conditions. These phenomena
can be ascribed to the property conversion of the governing equation from the elliptic (n > v/(l + v))
to parabolic (n = v/(l +v)) or hyperbolic type (n < v/(1 +v)). As illustrative examples, the Green
functions are ascertained for a half plane subjected to a normal and a shear forces, respectively. It
is found that the stress distribution for symmetric 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 compressive normal force. Copyright © 1996
Elsevier Science Ltd.
