J-vector theory for simulation of rectilinear crack growth

The J-vector theory is for the description of crack growth in materials in general. The present formulation of the J-vector theory is for rectilinear crack growth in a two-dimensional solid, but it can be written for a curvilinear case. The more general form of the J-vector theory predicts the amount and the direction of crack growth. Thus this new theory is an extension to the J-integral concept. The fundamental idea of the J-vector theory is the mathematical separation of the body Vb into two different subdomains denoted by Wb(t) and Gb(t). The subdomain Gb(t) encloses the crack tip and the fracture process zone. It is imagined to be attached to the crack tip and to move with the growing crack.