Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies (1902.05922v1)

Abstract: The phase-field model (PFM) represents the crack geometry in a diffusive way without introducing sharp discontinuities. This feature enables PFM to effectively model crack propagation compared with numerical methods based on discrete crack model, especially for complex crack patterns. Due to the involvement of \phased field", phase-field method can be essentially treated a multifield problem even for pure mechanical problem. Therefore, it is supposed that the implementation of PFM based on a software developer that especially supports the solution of multifield problems should be more effective, simpler and more efficient than PFM implemented on a general finite element software. In this work, the authors aim to devise a simple and efficient implementation of phase-field model for the modelling of quasi-static and dynamic fracture in the general purpose commercial software developer, COMSOL Multiphysics. Notably only the tensile stress induced crack is accounted for crack evolution by using the decomposition of elastic strain energy. The width of the diffusive crack is controlled by a length-scale parameter. Equations that govern body motion and phase-field evolution are written into different modules in COMSOL, which are then coupled to a whole system to be solved. A staggered scheme is adopted to solve the coupled system and each module is solved sequentially during one time step. A number of 2D and 3D examples are tested to investigate the performance of the present implementation. Our simulations show good agreement with previous works, indicating the feasibility and validity of the COMSOL implementation of PFM.

• The paper presents a detailed implementation of phase‐field models in COMSOL, simplifying fracture simulation with a smooth phase‐field approach.
• The authors use a staggered solution scheme with elastic strain energy decomposition to reliably simulate tensile crack propagation.
• Extensive 2D and 3D case studies validate the model against benchmarks, highlighting the effects of key parameters on crack patterns and load responses.

Phase Field Modeling of Crack Propagation: A COMSOL Implementation

The paper under review presents a methodical approach to implementing phase-field models (PFM) for simulating quasi-static and dynamic crack propagation within the COMSOL Multiphysics software environment. The authors Shuwei Zhou, Timon Rabczuk, and Xiaoying Zhuang endeavor to illustrate the effectiveness of the phase-field method in modeling fractures, emphasizing the simplification and efficiency that can be gained by leveraging a software framework that inherently supports multifield problems.

Contribution and Approach

The primary contribution of this paper lies in its detailed implementation of PFM for fracture modeling using COMSOL, a popular choice for complex simulations involving multifield interactions. Unlike discrete crack models or alternative methods like XFEM that can be computationally intensive due to the need to track crack surfaces explicitly, the phase-field approach presents cracks as smooth transitions in a scalar field, simplifying the numerical treatment of crack propagation.

The authors utilize a staggered solution scheme within COMSOL, capitalizing on its multifield capabilities. They decompose the elastic strain energy into tensile and compressive components to ensure cracks propagate only under tensile stresses. This decomposition is critical in accurately simulating fracture mechanics.

Numerical Results and Observations

Extensive numerical experiments, both in two-dimensional and three-dimensional settings, form the backbone of this work’s validation efforts. The selected cases include well-known benchmarks such as the three-point bending tests and dynamic shear loading scenarios inspired by the Kalthoff experiments.

Key numerical findings and observations can be summarized as follows:

• The reported crack patterns and load-displacement curves corroborate well with established results across different fracture benchmarks.
• The influence of the phase-field’s length scale parameter, mesh density, time-step size, and critical energy release rate on the simulation outcomes were thoroughly investigated. Smaller length scale parameters result in less diffused crack representation, whereas larger mesh sizes tend to overestimate the peak loads.
• The staggered scheme used in COMSOL efficiently resolved the coupled fields, allowing the system to adapt to both quasi-static and dynamic loading conditions. This adaptability is crucial for the multifaceted nature of real-world fracture applications.

Implications and Future Directions

This work underscores the utility of commercial software for advancing crack modeling techniques, particularly by simplifying implementation through built-in support for coupling multiple physical phenomena. Researchers and engineers can extend this baseline implementation towards more intricate fracture mechanics problems, including hydraulic fracturing or applications involving thermal, fluid, or chemical fields.

Future research could explore the application potential further, perhaps investigating the interaction of phase-field models with real-time data acquisition processes such as in-situ load measurements during testing or the integration with machine learning algorithms to predict complex crack trajectories. Moreover, the efficient treatment of multifield coupling in a computationally cost-effective way remains a promising avenue for ongoing paper.

In conclusion, this paper presents a robust implementation of phase-field modeling within COMSOL, achieving significant streamlining of multi-scale crack propagation simulations. By doing so, it opens up new pathways for advanced modeling in engineering mechanics and material sciences.