A Three-Scale Generalized FEM for the Simulation of 3-D Crack Propagation
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This work addresses the challenge of simulating 3-D cracks that are significantly smaller than the overall analysis domain, motivated by two key applications: reflective cracking in asphalt-overlaid jointed concrete airfield pavements and mechanically short crack propagation in cyclically loaded structural components. In the first application, initial crack lengths of a few millimeters exist within domains exceeding 10 meters (required for modeling aircraft landing gear loads) [1]. The goal of the second application is to determine the largest non-propagating crack under cyclic loading, which can be just a few microns. Accurate Stress Intensity Factors (SIFs) in either case require meshes with elements several orders of magnitude smaller than the analysis domain, which in turn leads to large and ill-conditioned matrices, even in the case of p-hierarchical Finite Element Methods [2]. A three-scale Generalized Finite Element Method (GFEM3) approach is proposed to overcome these challenges. It combines the GFEM with global-local enrichments (GFEMgl) [3] and classical sub-modeling methods. The GFEMgl breaks the problem into two scales and provides boundary conditions for sub-models defined along the crack front. These models are solved in parallel, and their resulting SIF functions are combined to define unique SIF functions along the entire crack front. A numerical experiment demonstrating the main features, accuracy, and computational performance of the proposed three-scale GFEM is presented. REFERENCES [1] M. Beheshti, M.H.C. Bento, C.S. Ramos, C.A. Duarte, D.R. Brill, H. Ozer. Analysis of Reflective Cracking in Asphalt Overlaid Jointed Concrete Airfield Pavements Using a 3-D Generalized Finite Element Approach, International Journal of Pavement Engineering, 25(1):2346291, 2024. [2] B. Andersson, J. J. Greer, Creation and verification of world’s largest KI-databases for multiple cracks at a countersunk and straight-shank hole in a plate subject to tension, bending, and pin-loading, in: 35th ICAF Conference and 29th ICAF Symposium, Nagoya, Japan, 2017. [3] J. Pereira, D.-J. Kim, C. Duarte, A two-scale approach for the analysis of propagating three-dimensional fractures, Computational Mechanics 49 (1) (2012) 99–121. doi:10.1007/s00466-011- 0631-4.
