Non-local theory solution to a 3-D rectangular crack in an infinite transversely isotropic elastic material

详细信息    查看全文

• 作者：Hai-Tao Liu ; Zhen-Gong Zhou ; Lin-Zhi Wu
• 关键词：Mechanics of solids ; Non ; local theory ; 3 ; D rectangular crack ; The lattice parameter
• 刊名：Meccanica
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：50
• 期：4
• 页码：1103-1120
• 全文大小：875 KB
• 参考文献：1. Rubio-Gonzalez, C, Mason, JJ (1999) Response of finite cracks in orthotropic materials due to concentrated impact shear loads. ASME J Appl Mech 66: pp. 485-491 CrossRef
  2. Shol, CW, Lee, KY (2001) Dynamic response of subsurface interface crack in multi-layered orthotropic half-space under anti-plane shear impact loading. Int J Solids Struct 38: pp. 3563-3574 CrossRef
  3. Zhu, BJ, Qin, TY (2007) Hypersingular integral equation method for a three-dimensional crack in anisotropic electro-magneto-elastic bimaterials. Theor Appl Fract Mech 47: pp. 219-232 CrossRef
  4. Li, YS, Feng, WJ, Xu, ZH (2009) A penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer. Meccanica 44: pp. 377-387 CrossRef
  5. Qin, TY, Noda, NA (2003) Stress intensity factors of a rectangular crack meeting a bimaterial interface. Int J Solids Struct 40: pp. 2473-2486 CrossRef
  6. Zhou, ZG, Wang, B (2006) An interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Meccanica 41: pp. 79-99 CrossRef
  7. Ueda, S (2008) Transient thermoelectroelastic response of a functionally graded piezoelectric strip with a penny-shaped crack. Eng Fract Mech 75: pp. 1204-1222 CrossRef
  8. Itou, S (2007) Transient dynamic stress intensity factors around two rectangular cracks in a nonhomogeneous interfacial layer between two dissimilar elastic half-spaces under impact load. Acta Mech 192: pp. 89-110 CrossRef
  9. Itou, S (2007) Dynamic stress intensity factors around a cylindrical crack in an infinite elastic medium subject to impact load. Int J Solids Struct 44: pp. 7340-7356 CrossRef
  10. Itou, S (2010) Dynamic stress intensity factors for two parallel interface cracks between a nonhomogeneous bonding layer and two dissimilar elastic half-planes subject to an impact load. Int J Solids Struct 47: pp. 2155-2163 CrossRef
  11. Hsu, WH, Chue, CH (2009) Mode III fracture problem of an arbitrarily oriented crack in an FGPM strip bonded to a homogeneous piezoelectric half plane. Meccanica 44: pp. 519-534 CrossRef
  12. Zhou, ZG, Liu, JY, Wu, LZ (2012) Basic solutions of a 3-D rectangular limited-permeable crack or two 3-D rectangular limited-permeable cracks in piezoelectric materials. Meccanica 47: pp. 109-134 CrossRef
  13. Zhou, ZG, Hui, JF, Wu, LZ (2008) Basic solution of a mode-I limited-permeable crack in functionally graded piezoelectric materials. Meccanica 43: pp. 21-35 CrossRef
  14. Shi, PP, Sun, S, Li, X (2013) Arc-shaped interfacial crack in a non-homogeneous electro-elastic hollow cylinder with orthotropic dielectric layer. Meccanica 48: pp. 415-426 CrossRef
  15. Eringen, AC, Kim, BS (1974) Stress concentration at the tip of crack. Mech Res Commun 1: pp. 233-237 CrossRef
  16. Eringen, AC Non-local polar field theory. In: Eringen, AC eds. (1976) Continuum physics. Academic Press, New York
  17. Edelen, DGB Non-local field theory. In: Eringen, AC eds. (1976) Continuum physics. Academic Press, New York
  18. Green, AE, R
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Civil Engineering
  Automotive and Aerospace Engineering and Traffic
  Mechanical Engineering
  
• 出版者：Springer Netherlands
• ISSN：1572-9648

文摘

The non-local theory solution to a 3-D rectangular crack in an infinite transversely isotropic elastic material is proposed by means of the generalized Almansi’s theorem and the Schmidt method in the present paper. By using the Fourier transform and defining the jumps of displacement across the crack surface as the unknown variables, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of displacement across the crack surface are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack and the lattice parameter of the material on the stress field near the crack edges. Unlike the classical solution, the present solution is no stress singularity along the rectangular crack edges, i.e. the stress field near the rectangular crack edges is finite. Therefore, we can use the maximum stress as a fracture criterion.