THE SINGULAR ELASTOSTATIC FIELD DUE TO A CRACK IN RUBBER-LIKE MATERIALS

Within the framework of finite-strain elastostatics an asymptotic anal ysis is carried out in order to calculate the singular field near the crack tip in a slab under conditions of plane deformation. A class of Ogden-Ball hyperelastic rubberlike materials and general loading condi tions ensuring vanishing tractions on the crack faces near the crack t ip are considered. It is shown that the singular deformation field nea r the crack tip can be specified by applying a rigid body rotation wit h a subsequent parallel translation to a so-called canonical field. Th e adjective canonical is adopted here to denote the field with symmetr ically opening crack faces, just resembling the displacement field of the symmetric mode in linear elastic fracture mechanics. No analogy wi th the antisymmetric mode is possible, and the crack equilibrium crite rion requires only one stress intensity factor to be determined.