Evaluation of energy contributions in elasto-plastic fracture: A review of the configurational force approach

• We discuss the role of the material (configurational) force approach in elasto-plasticity at small and finite strains.
• A thermodynamic framework for the configurational and deformational motion in elasto-plasticity is considered.
• The separation of total dissipation in terms of the change in elastic energy and material dissipation is investigated.
• The material force is path independent if all terms of the momentum balance are included in the variational formulation.
• The momentum balance equation is obtained by assuming different parts of the strain energy density function.

This paper discusses the role of the material or rather configurational force approach in elastic–plastic materials with a pre-cracked configuration and gives an overview of some recent numerical investigations of the crack tip field. On the theoretical side, a consistent thermodynamic framework for the combined configurational and deformational motion in elasto-plastic continua at small and finite strains is discussed. Furthermore, the study researches the separation of the total dissipation in terms of the change in elastic energy and in terms of the material dissipation by a configurational change obtained from the global energy momentum balance. On the numerical side, an equivalent general expression of the vectorial material forces is derived from the weak form of the energy momentum balance. For the sake of simplicity, all results are obtained neglecting dynamic and thermo-mechanical phenomena. The computations are applied to a stationary crack in a circular pre-cracked domain and a compact tension specimen under plasticity condition. The results show that the material force approach remains path independent only if all components of the momentum balance equation are properly included into the corresponding variational formulation. In addition, the cohesive fracture theory is combined with the material force approach in order to increase the clarity of the interpretation of the approach in engineering applications. Correspondingly, the results obtained from the compact tension specimen with three different free energy functions are compared to the conventional J-integral method and to experimental results available from a previous study. The contributions of this study are threefold. First, the path dependency of the material force approach in elasto-plastic continua is found to be considerably depending on the so-called material body forces. Secondly, interpretation of the induced material dissipation forces in the definition of the crack driving forces is not explicitly clear but they play an important role in case of path independency. Finally, with further analyses on compact tension examples, it is shown that the introduced energy functions in the material momentum balance yield a difference for the evaluation of the material force approach and the traditional J-integral.