Mixed-mode separation in dynamic fracture mechanics: New path independent integrals

This paper presents a theoretical and numerical analysis of mixed-mode separation in fracture dynamics, based on new path independent integrals. The M-integral method proposed by Chen and Shield is generalized for dynamic fracture applications. Strain energy density is expressed as a function of the actual displacement field and of an auxiliary kinematically admissible field. On the other hand, the concept of the G circle minus- integral developed by Destuynder using the Rice J-integral is extended to dynamic problems. Introducing the same concept in the M-integral formulation leads to the new path-independent integral M circle minus in elastodynamics. Numerical tests give us accurate results of separated mode.