دانلود رایگان مقاله مدل سازی سه بعدی ترک خوردگی در مواد جامد با روش المان محدود

Abstract

A three dimensional (3D) augmented finite element method (AFEM) for modeling arbitrary cracking without the need of additional degree of freedom (DoFs) or phantom nodes is presented. Four or three internal nodes are employed to explain displacement jump due to the weak and strong discontinuity. In this method, damage and discontinuity are treated from a weak discontinuity to a strong one without additional degree of freedom and without explicit representation of the crack. A fully condensed elemental equilibrium equations as mathematical exactness in the piece-wise linear sense is explicitly derived within AFEM formulation. The method is implemented in ABAQUS 4-node tetrahedron user element with a local crack tracking method for crack path detection. Through some numerical examples, it is shown that the 3D AFEM can accurately and efficiently crack initiation and propagation.

6. Conclusions

In the current paper, arbitrary cracking in solids is simulated by 3D AFEM without the need for additional DoFs. The formulation is implemented into UEL subroutine of ABAQUS with a 4- node tetrahedron element. The 3D AFEM introduces internal node-pairs with normal displacements as internal nodal DoFs. The internal node-pairs are ultimately condensed at elemental level using a consistency-check based condensation algorithm. Hence, the crack displacements are natural results of the elemental equilibrium. The crack surface evolution is computed and recorded using a local tracking technique. Within several numerical examples, the capabilities of 3D AFEM is demonstrated. Particularly, the global instability (snap-back) numerical example (double notch shear beam) and cracking in cross ply composite laminate show the effectiveness of AFEM. Also, it should be mentioned that augmentation procedure can be extended to other types of 3D elements.