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Research Papers

Augmented Cohesive Elements for Efficient Delamination Analyses of Composite Laminates

[+] Author and Article Information
H. Qiao, W. Q. Chen

Department of Engineering Mechanics,  Zhejiang University, Hangzhou, China 310027

Q. D. Yang1

Department of Mechanical and Aerospace Engineering,  University of Miami, Coral Gables, FL 33124qdyang@miami.edu

J. Lua

 Global Engineering and Materials, Inc., 1 Airport Place, Suite 1, Suite 200, Princeton, NJ 08540

For this case, the conventional GI and SDI are much worse than the mixed GI& scheme. Detailed discussion can be found in Ref. [19].

Dassault System Simulia Corporation, Providence, RI 02909.

In a commercial software package such as ABAQUS, this can be conveniently done through the use of “offset” function in shell section definition.

1

Corresponding author.

J. Eng. Mater. Technol 133(4), 041010 (Oct 20, 2011) (8 pages) doi:10.1115/1.4004694 History: Received March 16, 2011; Revised July 12, 2011; Published October 20, 2011; Online October 20, 2011

In this paper, a new type of cohesive element that employs multiple subdomain integration (MSDI) for improved cohesive stress integration accuracy of bonded plate/shell elements has been formulated. Within each subdomain, stress integration is compatible with existing schemes such as Gaussian integration (GI), Newton–Cotes integration, or the mixed Gaussian and subdomain integration (mixed GI&SDI). The numerical accuracy, efficiency, and robustness of this element when employing three integration methods for MSD cohesive stress integration have been evaluated and compared through a benchmark mode-I fracture problem of bonded double-cantilever plates. The MSDI offers at least 50% improvement of numerical accuracy as compared to the best integration method in literature and has the best numerical robustness. This significant improvement pushes the structural mesh size restriction from limiting size of 1/3–1/5 cohesive zone length to 1.5–2 times the cohesive zone length. The formulation is very easy to be implemented into any finite element programs including commercial packages. Furthermore, this formulation enables the use of dual-mesh for delamination analyses of bonded structural shells/plates, which is of practical importance because it greatly reduces the burden of mesh generation for complicated composite structures. It has also been demonstrated that using high-order shell/plate elements can improve the numerical accuracy in general because the nonlinear deformation profile permitted by this type of elements can better describe the nonlinear deformation in the crack-tip element (partially bonded elements).

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Numerical oscillations in cohesive fracture analysis of bonded double-cantilever plates with traditional GI, NCI, and mixed GI&SDI integration scheme

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Figure 2

Edge view of two plates, each discretized into three shell elements, bonded by three cohesive elements (le /lcoh  > 1). As the delamination crack propagates from right to left, two situations can cause significant numerical oscillations. In (a), the entire cohesive zone is within a single element and the two SDI integration points is not adequate for stress integration, resulting underestimate of applied load; in (b), as the cohesive zone crosses a bonded node-pair, the GI scheme used in the element immediately ahead of the crack-tip element results in significant contact at the left node-pair of the element, resulting in significant overload.

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Figure 3

(a) Definition of the nonlinear 3D CZM element abutting two 8-node quadrilateral shell elements. The thickness of the bonded area is exaggerated for better rendering of the midplane (S) that is used for local coordinates (t-s-n) definition. (b) the multiple subdomains ( ①- ⑨) used for cohesive stress integration. Linear cohesive stress integration with GI, NCI, and mixed GI&SDI can be used within each subdomain.

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Figure 4

(a) Two S8R5 shell elements bonded by a cohesive element under symmetric mode-I loading (displacement controlled). (b) The analytical solution of load-displacement curve as compared by numerical solutions obtained via various integration schemes.

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Figure 5

The bonded double-cantilever plates for cohesive fracture analysis. The upper and bottom plates are modeled with high-order shell elements (S8R5), which are bonded by MSDI cohesive elements.

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Figure 6

(a) Effective reduction of numerical oscillation due to the use of MSDI and high-order shell element. (b) Predicted load-displacement curves using MSDI for four different normalized mesh sizes.

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Figure 7

(a) Averaged numerical error as a function of normalized mesh size as compared to mixed GI&SDI method, showing overall accuracy improvement due to MSDI is >50% over mixed GI&SDI; and (b) comparison of CPU times showing the MSDI with mixed GI&SDI for cohesive stress integration is on average the most efficient method

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Figure 8

(a) Load-displacement curves for normalized mesh size of le /lcoh  = 2.28 obtained with different normalized subdomain integration sizes (lint /lcoh ); (b) comparison of load-displacement curve between staggered and conformed integration mesh

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