On the partition of fracture energy in constitutive modelling of quasi-brittle materials

Most constitutive models for quasi-brittle materials ignore the fact that the measurable fracture energy represents more than one dissipative mechanism, including those from the creation of new surface areas and frictions between surfaces. Specifically, these models “see” the measurable fracture energy as one that comes only from the creation of new surface area. However, experimental deduction by Bažant indicates that the frictional dissipation is not at all negligible, even in mode I failure, where it contributes an energy loss of around 50–75% to the total dissipation budget. Here we study the consequences of this simplification by adopting simple local and nonlocal damage models, which include a new powerful parameter that represents the measurable partition of the dissipation. It is found that the oversight of frictional dissipation can lead to a critical over-prediction of both the magnitude and the spreading of damage.