In this paper, an improved version of path independent integral is derived to predict crack growth, in both, isotropic and orthotropic materials. The proposed T and A integrals allow us to compute the energy release including the effects of temperature variation and mechanical loads applied to the crack lips. The formulation is based on Noether’s theorem and strain energy density derived from Lagrangian and Eulerian configurations. By introducing an appropriate auxiliary mechanic field, the mixed-mode fracture problems can be easily addressed, for which the stress intensity factors can be efficiently computed. The developed numerical procedure is implemented in the finite element software Cast3m, in order to analyze cracked isotropic solids under various boundary and loading conditions, in opening, shear and mixed modes. In all these applications, the proposed integrals have shown to be path independent. The accuracy and the efficiency of the proposed approach are verified for orthotropic cracked bodies, such as timber material.