The breakthrough, published in the scientific journal Computational Mechanics, introduces the Double Gradient Correction Method (DGCM). This novel mathematical approach efficiently resolves the tendency of current computational models to overestimate crack area in fracture problem simulations.
Phase-field based models are crucial in modern engineering for predicting crack propagation and material failure under stress. However, they often suffer from a numerical artifact known as "localized deformation," which artificially saturates the damage variable and distorts calculations, leading to the assumption of a larger cracked area than reality.
The DGCM method leverages the fundamental physical principle of fracture energy equipartition. The researchers, including Dr. Miguel Castillón and Profs. Javier Segurado and Ignacio Romero, observed that while calculation errors severely affect the direct damage variable, the energy associated with its spatial gradient remains largely unaltered. By doubling the contribution linked to the spatial gradient of the damage variable, a more precise estimation of the fracture surface is achieved.
Validation tests have demonstrated that this approach significantly reduces the deviations found in conventional simulation methods, optimizing structural failure predictions without increasing computational cost. "This new mathematical approach allows for a more reliable analysis of material behavior near their failure limit, reducing numerical errors without adding computational complexity, and is applicable to three-dimensional models," stated Dr. Castillón.
The code for implementing the DGCM method has been released openly under a free license, facilitating its integration into standard industrial simulation tools. The repository is hosted on GitHub and permanently archived on Zenodo. Numerical simulations were performed using PhaseFieldX, an open-source library built on the FEniCSx finite element framework, ensuring complete reproducibility of the results.
