This paper presents a conforming augmented finite element method (C-AFEM) that can account for arbitrary cracking in solids with similar accuracy of other conforming methods, but with a significantly improved numerical efficiency of about ten times. We show that the numerical gains are mainly due to our proposed new solving procedure, which involves solving a local problem for crack propagation and a global problem for structural equilibrium, through a tightly coupled two-step process. Through several numerical benchmarking examples, we further demonstrate that the C-AFEM is more accurate and mesh insensitive when compared with the original A-FEM, and both C-AFEM and A-FEM are much more robust and efficient than other parallel methods including the extended finite element method (XFEM)/generalized finite element (GFEM) and the conforming embedded discontinuity method.
A Conforming Augmented Finite Element Method for Modeling Arbitrary Cracking in Solids
Coral Gables, FL 33124
Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received February 20, 2019; final manuscript received March 11, 2019; published online April 12, 2019. Assoc. Editor: Yonggang Huang.
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Ma, Z., Yang, Q., and Su, X. (April 12, 2019). "A Conforming Augmented Finite Element Method for Modeling Arbitrary Cracking in Solids." ASME. J. Appl. Mech. July 2019; 86(7): 071002. https://doi.org/10.1115/1.4043184
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