# [1]钟志鹏,万水.考虑裂纹接触摩擦的逐点Lagrange乘子法[J].东南大学学报(自然科学版),2012,42(5):994-999.[doi:10.3969/j.issn.1001-0505.2012.05.035] 　Zhong Zhipeng,Wan Shui.Point-by-point Lagrange multiplier method for modeling interface cracks with contact and friction[J].Journal of Southeast University (Natural Science Edition),2012,42(5):994-999.[doi:10.3969/j.issn.1001-0505.2012.05.035] 点击复制 考虑裂纹接触摩擦的逐点Lagrange乘子法() 分享到： var jiathis_config = { data_track_clickback: true };

42

2012年第5期

994-999

2012-09-20

## 文章信息/Info

Title:
Point-by-point Lagrange multiplier method for modeling interface cracks with contact and friction

Author(s):
School of Transportation, Southeast University, Nanjing 210096, China

Keywords:

O346.1
DOI:
10.3969/j.issn.1001-0505.2012.05.035

Abstract:
In order to solve the stress near the crack tip accurately, a new algorithm—point-by-point Lagrange multiplier method(PLMM)for solving the crack contact problem in an infinite plate is proposed. First, the Lagrange multiplier is transformed to a local coordinate system. Then, the iterative solution of normal and tangential multiplier forces is solved by using the Gauss-Seidel iteration method and the constraint modification of the tangential multiplier is made. After the calculation of all point multiplier forces completed, they are transformed to a global coordinate system to solve displacements iteratively. Compared with the conditional contact algorithms, the PLMM without finding the inverse global stiffness matrix requires less computer storage. The stress intensity factors(SIFs)for the center cracked plate under compression and shear and the center interface crack under shear traction are calculated by the PLMM method, and the calculation results show good agreement with the results in literature. The influences of the friction coefficients on the displacement field, contact zone, and stress fields near the crack tip of the Comninou contact model are studied. The results show that the effect of contact on the distribution of normal stress is great and the SIF may be overestimated without considering crack surface contact.

## 参考文献/References:

[1] Chen X H,Huang W,Qian Z D.Interfacial behaviors of epoxy asphalt surfacing on steel decks [J].Journal of Southeast University:English Edition, 2007,23(4):594-598.
[2] Rice J R,Sih G C.Plane problems of cracks in dissimilar media [J].Journal of Applied Mechanics,1965,32(2):418-423.
[3] Comninou M,Schmueser D.The interface crack in a combined tension-compression and shear field [J].Journal of Applied Mechanics, 1979,46(2):345-348.
[4] Qian W,Sun C T.A frictional interfacial crack under combined shear and compression [J].Composites Science and Technology, 1998,58(11):1753-1761.
[5] Collombet F,Lalbin X,Bonini J,et al.Contact impact techniques for the study of impacted laminated structures [J].Recent Advances in Contact Mechanics, 2008,28(4/5/6/7/8):171-184.
[6] Bruno D,Greco F,Lonetti P.A coupled interface-multilayer approach for mixed mode delamination and contact analysis in laminated composites [J].International Journal of Solids and Structures, 2003,40(1):7245-7268.
[7] Giner E,Sabsabi M,Fuenmayor F J.Calculation of K in crack face contacts using X-FEM.Application to fretting fatigue [J].Engineering Fracture Mechanics,2011,78(2):428-445.
[8] Nemat-Nasser S,Horii H.Compression-induced nonplanar crack extension with application to splitting,exfoliation and rockburst [J].Journal of Geophysical Research, 1982,87(B8):6805-6821.
[9] Avraham D,Leeslie B S.Shear loaded interface crack under the influence of friction:a finite difference solution [J].International Journal for Numerical Methods in Engineering, 2004,59(13):1749-1780.
[10] 郭小明,赵惠麟.工程结构接触问题的研究及进展[J].东南大学学报:自然科学版,2003,33(5):577-582.
Guo Xiaoming,Zhao Huilin.Study on contact problems in engineering structures [J].Journal of Southeast University:Natural Science Edition, 2003,33(5):577-582.(in Chinese)
[11] 梁国平.有限元语言[M].北京:科学出版社,2009.
[12] Shi X Q,Zhang X R,Pang H L.Determination of interface fracture toughness of adhesive joint subjected to mixed-mode loading using finite element method [J].International Journal of Adhesion & Adhesives, 2006,26(4):249-260.

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