Cracks in rubber

The onset of crack propagation in rubber is studied computationally by using the softening hyperelasticity approach. The basic idea underlying the approach is to limit the capability of a material model to accumulate energy without failure. The latter is done by introducing a limiter for the strain energy density, which results from atomic/molecular considerations and can be interpreted as the average bond energy or the failure energy. Including the energy limiter in a constitutive description of material it is possible to enforce softening and, consequently, allow tracking the onset of structural instability corresponding to the onset of material failure. Specifically, initiation of crack propagation is studied in the case of a thin sheet of a rubber-like solid under the hydrostatic tension. The large deformation neo-Hookean material model enhanced with the energy limiter is used for finding the critical tension corresponding to the onset of static instability of the sheet, i.e. the onset of fracture propagation. The influence of the crack sharpness and length on the critical load is analyzed. It is found that material is sensitive to the crack sharpness when the shear modulus is significantly greater than the average bond energy. The sensitivity declines when the value of the shear modulus approaches the value of the failure energy. Roughly speaking, softer materials are less sensitive to cracks than more brittle materials where the brittleness is defined as a ratio of the shear modulus to the failure energy. It is also found that the critical tension is proportional to the inverse square root of the crack length for more brittle materials. The latter means that the Griffith theory based on the linearized elasticity is also applicable to softer materials undergoing large deformations. Unfortunately, the applicability of the Griffith theory is restricted to cracks with equivalent sharpness only.