Identification of fracture models based on phase field for crack propagation in heterogeneous lattices

In engineering practice, various materials having varying properties can be combined to form robust and economical composite building materials. Other materials can be directly manufactured with desired properties by recent additive manufacturing (3D printing) techniques. Majority of these materials are heterogeneous. In such materials, macro cracks develop from micro cracks which initiate at the microscale mainly due to local stress concentrations or at the interfaces. The durability of various civil structures is largely dependent on the strength of the material used for their construction, consequently, studying crack propagation in such media is of high importance. Unfortunately, direct numerical simulations involving an explicit description of microcracks and all heterogeneities is so far not tractable and neither efficient to study cracking in engineering applications.

Therefore, it is highly important to construct homogenized models able to reproduce accurately the damage in the structure and involving reasonable computational times. In a recent publication, a group of researchers from Multiscale Modeling and Simulation Laboratory at University Paris-Est, France: Dr. Nhu Nguyen and Professor Julien Yvonnet in collaboration with Professor Julien Réthoré at Ecole Centrale de Nantes and Dr. A. B. Tran at Hanoi University of Civil Engineering investigated the construction of a homogeneous medium equivalent to a heterogeneous one under quasi-brittle fracture in the case of non-separated scales. Their work is currently published in the research journal, Computational Mechanics.

The research team employed the phase field method at the micro-scale level. In addition, at the scale of the homogeneous medium, another phase field model either isotropic or anisotropic, depending on the microscale crack length and on the underlying microstructure, was assumed. Eventually, the coefficients of the unknown phase field model for the homogeneous model was identified through the mechanical response of a sample subjected to fracture whose microstructure was fully described and estimated numerically.

The authors reported that the identified models could reproduce both the mechanical force response as well as overall crack paths with good accuracy in other geometrical configurations than the one used to identify the homogeneous model. In fact, using their approach, several numerical examples, involving cracking in regular lattices of both hard particles and pores, were presented to demonstrate the potential of the technique.

In summary, the study demonstrated a new procedure to construct an equivalent homogeneous model for heterogeneous lattices subjected to crack propagation in the case of non-separated scales. Basically, the researchers proposed to use at the scale of the homogeneous medium phase field models, whose parameters were identified through numerical crack propagation tests in fully heterogeneous samples. Overall, results showed that their homogeneous model was able to reproduce both force response and crack paths subject to that situation.