Rectilinear crack growth in hyperelastic materials

Rectilinear crack growth in hyperelastic materials is considered. The crack growth process is studied by using the well-known law of continuum mechanics; the law of kinetic energy. The key concept of the derivation is the separation of the volume of the body into two different parts denoted by omega and gamma. The latter region encloses the crack tip and it is imagined to be attached to the crack tip and therefore moving through the body with growing crack. By this procedure a line-integral called here as the J-vector is derived. It is an extension to the well-known J-integral. In contrast to the J-integral the J-vector is associated with crack growth. The quasi-static part of the J-vector is shown to be path-independent. A simple model for crack growth is introduced. A relationship between the potential energy and the J-vector is derived. It has the same form as was proposed for the relation between the potential energy and the J-integral which is often used in the verification of the J-integral for the simulation of crack growth. This interpretation is strongly criticised.