|
|
- 2017
非均匀材料界面裂纹的Cell-Based光滑有限元法
|
Abstract:
为提高非均匀材料界面裂纹尖端断裂参数的求解精度，基于非均匀材料界面断裂力学、Cell-Based光滑有限元（Cell-SFEM）和非均匀材料的互交作用积分法，提出了求解非均匀材料界面裂纹尖端断裂参数的Cell-Based光滑有限元法，推导了基于Cell-Based光滑有限元法的非均匀材料的互交作用积分法，对非均匀材料间的界面裂纹尖端处正则应力强度因子进行了求解，并与参考解进行了比较，讨论了互交积分区域大小和光滑子元个数与正则应力强度因子的关系。数值算例结果表明：本方法具有很高的计算精度，对积分区域大小不敏感，可为设计、制造抗破坏非均匀材料提供依据。 In order to improve the precision of inhomogeneous material interface crack tip fracture parameters which based on the inhomogeneous material interface fracture mechanics, Cell-Based smoothed finite element method(Cell-SFEM) and inhomogeneous material interaction integral, the Cell-Based smoothed finite element method was put forward to work out the inhomogeneous materials interface crack tip fracture parameters, and the interaction integral of inhomogeneous material based on Cell-Based smoothed finite element method was deduced. The normalized stress intensity factor in inhomogeneous material interface crack tip was solved. Compared with the reference solution, the relationship between the sizes of interaction integral region, the number of smoothing element and normalized stress intensity factor was discussed. The results of numerical example show that this method has high computational accuracy. It is not sensitive to integral area size as its features, and it can provide the basis for design and manufacture anti-failure of inhomogeneous material. 国家自然科学基金（51178206）；吉林省科技厅基金（20160520064JH）
| [1] | GUO F N, GUO L C, HUANG K, et al. An interaction energy integral method for T-stress evaluation in nonhomogeneous materials under thermal loading[J]. Mechanics of Materials, 2015, 83:30-39. |
| [2] | YU T T, BUI T Q, LIU P, et al. Interfacial dynamic impermeable cracks analysis in dissimilar piezoelectric materials under coupled electromechanical loading with the extended finite element method[J]. International Journal of Solids and Structures, 2015, 67:205-218. |
| [3] | WILLIAMS M L. The stresses around a fault or crack in dissimilar media[J]. Bulletin of the Seismological Society of America, 1959, 49(2):199-204. |
| [4] | RICE J R. Elastic fracture mechanics concepts for interfacial cracks[J]. Journal of Applied Mechanics, 1988, 55(1):98-103. |
| [5] | DOLBOW J E, GOSZ M. On the computation of mixed-mode stress intensity factors in functionally graded materials[J]. International Journals of Solids and Structures, 2002, 39(9):2557-2574. |
| [6] | YU H J, WU L Z, GUO L C, et al. Interaction integral method for the interfacial fracture problems of two nonhomogeneous materials[J]. Mechanics of Materials, 2010, 42(4):435-450. |
| [7] | CHEN J S, WU C T, YOON S, et al. A stabilized conforming nodal integration for Galerkin mesh-free methods[J]. International Journal for Numerical Methods in Engineering, 2001, 50(2):435-466. |
| [8] | LIU G R, DAI K Y, NGUYEN T T. A smoothed finite element method for mechanics problems[J]. Computational Mechanics, 2007, 39(6):859-877. |
| [9] | WANG D, CHEN J S. A Hermite reproducing kernel approximation for thin-plate analysis with sub-domain stabilized conforming integration[J]. International Journal for Numerical Methods in Engineering, 2008, 74(3), 368-390. |
| [10] | EISCHEN J W. Fracture of nonhomogeneous materials[J]. International Journal of Fracture, 1987, 34:3-22. |
| [11] | BHATTACHARYA S, SINGH I V, MISHRA B K, et al. Fatigue crack growth simulations of interfacial cracks in bi-layered FGMs using XFEM[J]. Computational Mechanics, 2013, 52(4):799-814. |
| [12] | YU H J, WU L Z, GUO L C, et al. T-stress evaluations for nonhomogeneous materials using an interaction integral method[J]. International Journal for Numerical Methods in Engineering, 2012, 90(11):1393-1413. |
| [13] | GUO L C, NODA N. Modeling method for a crack problem of functionally graded materials with arbitrary properties-piecewise-exponential model[J]. International Journal of Solids and Structures, 2007, 44(21):6768-6790. |
| [14] | ZHOU L M, MENG G W, LI F, et al. Cell-based smoothed finite element method-virtual crack closure technique for a piezoelectric material of crack[J]. Mathematical Problems in Engineeing, 2015(3):1-10. |
| [15] | 周立明, 孟广伟, 王晖, 等. 基于光滑有限元的含裂纹复合材料的虚拟裂纹闭合法[J]. 湖南大学学报:自然科学版, 2014, 41(8):13-17. ZHOU L M, MENG G W, WANG H, et al. Virtual crack closure technique based on smoothed finite method for composite meterials with cracks[J]. Journal of Hunan University:Natural Sciences Edition, 2014, 41(8):13-17 (in Chinese). |
| [16] | LE C V, NGUYEN-XUAN H, ASKES H, et al. A cell-based smoothed finite element method for kinematic limit analysis[J]. International Journal for Numerical Methods in Engineering, 2010, 83(12):1651-1674. |
| [17] | NGUYEN-THOI T, PHUNG-VAN P, RABCZUK T, et al. Free and forced vibration analysis using the n-sided polygonal cell-based smoothed finite element method (nCS-FEM)[J]. International Journal of Computational Methods, 2013, 10(1):43-51. |
| [18] | LIU G R. A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods[J]. International Journal of Computational Methods, 2008, 5(2):199-236. |
| [19] | NGUYEN-XUAN H, LIU G R, NGUYEN-THOI T, et al. An edge-based smoothed finite element method for analysis of two-dimensional piezoelectric structures[J]. Smart Materials and Structures, 2009, 18(6):065015. |
| [20] | NGUYEN-THOI T, LIU G R, VU-DO H C, et al. A face-based smoothed finite element method (FS-FEM) for visco-elastoplastic analyses of 3D solids using tetrahedral mesh[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(41-44):3479-3498. |
