A multi-level adaptive mesh refinement method for phase-field fracture problems

In finite element analysis, adaptive mesh refinement (AMR) has become a common practice to improve the accuracy of the numerical solution in sensitive or disturbed regions without having to refine the mesh in the entire domain. It is important to determine when, where, how much, and how the element size should be adjusted during the phase field fracture process in order to reduce the computational cost significantly without compromising accuracy. These questions are addressed in this study with introducing a novel adaptive mesh refinement technique. We approximate the distance between the field nodes in an existing mesh by assuming a uniform distribution of the nodes around the middle point of the elements. During the simulation, the middle point of each element is considered as a new field node and then remeshing is performed if the calculated node distance is greater than the maximum acceptable node distance based on the amount of damage. To illustrate the performance of the proposed approach, four numerical examples are considered and the results are compared with those of the conventional methods. It can be deduced that performing initial analysis on a coarse mesh and gradually adding the new field nodes as the crack propagates can significantly reduce the computational cost in comparison with the conventional methods without losing the accuracy and without requiring prior information on the crack propagation path. The other advantages of this technique include its excellent convergence, ease of implementation, applicability to irregular and regular meshes with no hanging nodes, no discontinuity between the elements, no need to calculate error measure function.

Automated summary

In finite element analysis, adaptive mesh refinement (AMR) is commonly used to improve numerical solution accuracy in specific regions without refining the entire mesh. This study introduces a novel AMR technique for determining when and how to adjust element size during phase field fracture analysis, reducing computational cost without compromising accuracy. The technique involves approximating distance between field nodes in an existing mesh and performing remeshing as the crack propagates. Numerical examples demonstrate that this approach significantly reduces computational cost and maintains accuracy without prior knowledge of the crack propagation path. The technique also offers advantages in terms of convergence, ease of implementation, and applicability to irregular meshes.