A BOUNDARY-LAYER APPROACH TO STRESS ANALYSIS IN THE SIMPLE SHEARING OF RUBBER BLOCKS

Rubbers are usually modeled as being perfectly incompressible. In the simple shear of rubber blocks, the normal stress components, therefore, contain an arbitrary constant pressure term to be determined from the boundary conditions. There is therefore a fundamental ambiguity in the determination of this pressure because the normal stresses are expected to be identically zero on different faces of the sheared block. It is proposed here that the stress distribution near a face should be determined by the normal stress boundary condition at that face and that this distribution is valid only within a short distance from the face, giving rise to boundary layers at the faces of the sheared block. At the intersection of these boundary layers it will be assumed that the stress is additive. It is further assumed that the stresses within the bulk of the material should be determined by treating the perfectly incompressible material as equivalent to a slightly compressible material. The form of slight compressibility adopted here is that usually assumed in the finite element simulation of rubbers. These reasonable assumptions give rise to a complex stress pattern within the block. The results are qualitatively similar to results obtained by other authors on using a finite element approach for a neo-Hookean material. The possible occurrence of cavitation at the corners of the block is also examined.