An Efficient A-FEM for Arbitrary Cracking in Solids
In this paper a new augmented finite element method (A-FEM) that can account for multiple, intra-elemental discontinuities in heterogeneous solids has been derived. It does not need the extra DoFs as in the extended finite element method (X-FEM), or the additional nodes as in the phantom node method (PNM). The new A-FEM employs four internal nodes to facilitate the calculation of subdomain stiffness and the crack displacements due to an intra-elemental discontinuity. It is shown that through a novel efficient solving algorithm the displacement DoFs associated with the internal nodes can be solved analytically as functions of the regular nodal DoFs for any piece-wise linear cohesive laws, which leads to a fully-condensed elemental equilibrium equation that is mathematically exact. The new formulation permits repeated elemental augmentation to include multiple interactive cracks within a single element, enabling a unified treatment of the evolution from a weak discontinuity, to a strong discontinuity, and to multiple intra-element discontinuities, all within a single element that employs standard DoFs only. The new A-FEMs capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples. It has been demonstrated that the new A-FEM achieved more than two orders of magnitude improvement in numerical accuracy, efficiency, and robustness, compared to the X-FEM.
Augmented FEM Extended FEM Fracture Cohesive model Numerical simulation
Qingda Yang Wei Liu Xian-Yue Su
Dept.of Mechanical and Aerospace Engineering,University of Miami,Coral Gables,FL 33124.USA Dept.of Mechanical and Aerospace Engineering,University of Miami,Coral Gables,FL 33124.USA;Dept.of M Dept.of Mechanics & Aerospace Engineering,Peking University,Beijing 100871,China
国际会议
北京
英文
1-10
2013-06-16（万方平台首次上网日期，不代表论文的发表时间）