Fictitious Rough Crack Model (FRCM): A Smeared Crack Modelling Approach to Account for Aggregate Interlock and Mixed Mode Fracture of Plain Concrete

The intention of this paper is to clarify the mechanisms of mixed mode fracture and shear stress transfer in plain concrete. To capture these scarcely explored phenomena, a new mechanical formulation is proposed called the fictitious rough crack model (FRCM). The FRCM considers mode I deformations to control crack formation and residual tensile stress transfer, while mode II deformations are assumed to induce shear stress transfer along the crack surfaces and compressive normal stresses attributed to aggregate interlock. The fundamental idea of the FRCM is to combine these tension-softening and shear-transfer laws and to superimpose the emerging shear and normal stresses of both mechanisms in the crack. The paper illustrates the analytical development of the FRCM and its numerical implementation. Three well-known experimental benchmark problems (concrete panel test series by Nooru-Mohamed and by Hassanzadeh as well as aggregate interlock test series by Paulay and Loeber) are numerically addressed to test plausibility of FRCM results. The numerical implementation of the FRCM is capable of simulating the transition from mode-I fracture to mixed-mode fracture in the structural response and is also able to predict the crack path with reasonable agreement.