A Numerical Method for Applying Cohesive Stress on Fracture Process Zone in Concrete Using Nonlinear Spring Element.

Aiming at the numerical simulation of the entire crack propagation process in concrete, a numerical method is proposed, in which cohesive stress on the fracture process zone (FPZ) is simulated and applied by a nonlinear spring element. Using displacement control, the cohesive stress values on the FPZ are obtained from solving a system of nonlinear equations through an iterative process. According to a crack propagation criterion based on initial fracture toughness, the approach adds the spring elements to finite element analysis when simulating mode I crack propagation in standard three-point bending notched concrete beams with different strengths, initial crack ratios (a0/D), and depths (D). The simulated load versus displacement (P-Delta) curves are performed to recalculate the fracture energy and verify the accuracy of cohesion in the proposed method. The simulated load versus crack mouth opening displacement (P-CMOD) curves are consistent with the previous experimental results. Subsequently, the variations of the FPZ length and the crack extension resistance (KR) curves are studied according to the proposed iterative approach. Compared with the existing methods using a noniterative process, the iterative approach generates a larger maximum FPZ length and KR curve where the FPZ length is mainly determined by the fracture energy, tensile strength, and geometry shape of the beam, and the KR curve is primarily determined by the fracture energy and FPZ length. The significant differences in numerical results indicate that the applying cohesion is essential in numerical simulation. It is reasonable to conclude that the proposed nonlinear spring element is more applicable and practical in the numerical simulation of the concrete mode I crack propagation process by improving the accuracy of the cohesion applied on the FPZ.