Asymptotic fields at the tip of a cohesive crack growing at bi-material interface

The most realistic method used today for the numerical simulation of concrete fracture is the cohesive crack model, introduceded by Barenblatt (1962) and Dugdale (1960) for elasto-plastic materials and by Hillerborg at al. (1976) for quasi-brittle materials. According to this method the cohesive stresses acting on the non-linear fracture process zone are decreasing functions of the displacement discontinuity. This function is assumed to be a material property through the use of a pre-defined softening law. As a consequence the contributions of the process zone to the effective stiffness matrix are not positive-definite and can induce loss of incremental solution uniqueness. In this case the Newton-Raphson equilibrium iteration fails. During the numerical simulation of a laboratory test the peak load is achieved when the process zone is not completely developed. This is due to the small size of the specimen in comparison to the length of the process zone. In this conditions the above mentioned problems can be overtaken by assuming the loading point displacement or the Crack Mouth Opening Displacement (shortened CMOD) as the control parameter. This assumption is sufficient to prevent loss of uniqness and therefore to determine the peak load and a first part of the global post-peak response. When a large scale problem is analysed a fully developed process zone appears when the global load is still in the pre-peak phase. In this conditions the Newton-Raphson procedure can fail before the peak load is reached even if the CMOD is assumed as control parameter. Barpi and Valente showed that this problems can be overtaken by enforcing the asymptoticfields proposed by Karihaloo and Xiao for the case of a cohesive crack growing in MixedMode (Mode I and II) conditions. In the present paper the above mentioned asymptotic fields are generalized to the case of a cohesive crack growing at bi-material interface. This enhancement allows us to obtain a morerealistic simulation of the fracture process occurring at the dam-foundations joint. Numerical results in the case of a gravity dam proposed as a benchmark by the International Commission for Large Dams are shown.