A phase-field lattice model (PFLM) for fracture problem: Theory and application in composite materials

In the present work, a phase-field lattice model (PFLM) is proposed to model fracture problems. The element deletion process and oversimplified failure criterion of the classical lattice model not only lead to a strong mesh sensitivity but also limit the method's application to various materials and fracture modes. Hence, a smeared form of crack is introduced into the lattice model to deal with these problems. The model exploits discontinuous discrete methods to model the propagation of three-dimensional cracks by characterizing the crack with a phase -field variable. Moreover, by regarding the crack propagation process as a multi-field problem composed of a displacement field and a phase-field, a flexible and robust algorithm is established, in which the crack path can be obtained directly by resolving the governing equations. Numerical simulations were performed and compared with the experimental results and other numerical models. It is shown that the PFLM can capture the main features of the fracture for both brittle and quasi-brittle materials. To further demonstrate the performance of the model, a mesoscale system of cement composite generated by computed tomography scanning technology was examined. The result demonstrates that the fracture of composite materials can also be well predicted.