3D implementation of push-out test in ABAQUS using the phase-field method

The phase-field method (PFM) localizes the damaged and broken material in concrete with a phase-field order parameter d , successfully avoiding the description of nonsmooth crack surfaces, as well as the pre-setting and tracking of complex crack extension paths. However, most works have focused on 2D and simple 3D problems of non-reinforced concrete due to the high computational cost. A 3D PFM is implemented in the commercial finite element code ABAQUS to model damage and quasi-brittle fractures in composite beam concretes. The damage problem is implemented in the user subroutines UMAT and HETVAL on account of the similarity between the evolution law of the order parameter and the heat transfer law. In addition, a FORTRAN file is used to define the relationships among the material properties. Through this approach, modeling, computational task submission, and post-processing are completed in the GUI of ABAQUS, and the internal nonlinear algorithms are adopted directly. The accuracy of the modeling method is verified by comparing with two classical experimental data in the literature, and the maximum load data and load-displacement curve are well fitted. Moreover, a 3D numerical model for the push-out test of the composite beam is developed. Simulation results are consistent with the test results, such as the trend of the load-displacement curve, the damage pattern of the concrete, and the stress condition of the shear bolts. The parametric analysis shows that the compressive and tensile strengths of the shear bonds can significantly affect the load bearing capacity of composite beams, whereas the material parameters of concrete have a limited influence, consistent with the previous experience. The PFM has proven its ability to handle complex quasi-brittle fracture of concrete, and the present work can provide a reference for modeling concrete cracks in engineering structures.