Material momentum tensor and path-independent integrals of fracture mechanics

Balance laws involving the material momentum tensor are studied. By convenient choice of the Lagrangian, the balance law of moment of material momentum is derived directly by considering rotations in material space. Then the balance law connected with the property of similarity of material space is obtained. Symmetry of physical and material momenta in both representations which are used is studied. Finally, the relations of the obtained balance laws (for the static case) to path-independent integrals of fracture mechanics are discussed.