Design of crack-resistant two-dimensional periodic cellular materials

Journal of Mechanics of Materials and Structures

Volumn 4, Issue 3, 2009, Pages 441-457

  Lipperman, Fabian ^a   Ryvkin, Michael ^a   Fuchs, Moshe B ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Design; Discrete fourier transform; Fracture toughness; Honeycombs

Indexed keywords

EID: 70350408670     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2009.4.441     Document Type: Article

References (23)

1. W. Bolton, Engineering materials technology, 3rd ed., Butterworth-Heinemann, Oxford, 1998.
2. J. Y. Chen, Y. Huang, and M. Ortiz, "Fracture analysis of cellular materials: a strain gradient model", J. Mech. Phys. Solids 46:5 (1998), 789-828.
3. S. Choi and B. V. Sankar, "A micromechanical method to predict the fracture toughness of cellular materials", Int. J. Solids Struct. 42:5-6 (2005), 1797-1817.
4. V. S. Deshpande, M. F. Ashby, and N. A. Fleck, "Foam topology: bending versus stretching dominated architectures", Acta Mater. 49:6 (2001), 1035-1040.
5. N. A. Fleck and X. Qiu, "The damage tolerance of elastic-brittle, two-dimensional isotropic lattices", J. Mech. Phys. Solids 55:3 (2007), 562-588.
6. M. B. Fuchs and M. Ryvkin, "Explicit exact analysis of infinite periodic structures under general loading", Struct. Multidiscip. O. 23:4 (2002), 268-279.
7. M. B. Fuchs, M. Ryvkin, and E. Grosu, "Topological alternatives and structural modeling of infinite grillages on elastic foundations", Struct. Multidiscip. O. 26:5 (2004), 346-356.
8. L. J. Gibson and M. F. Ashby, Cellular solids: structure and properties, 2nd ed., Cambridge University Press, Cambridge, 1997.
9. J. S. Huang and L. J. Gibson, "Fracture toughness of brittle honeycombs", Acta Metall. Mater. 39:7 (1991), 1617-1626.
10. F. Lipperman, M. Ryvkin, and M. B. Fuchs, "Fracture toughness of two-dimensional cellular material with periodic microstructure", Int. J. Fract. 146:4 (2007), 179-190.
11. F. Lipperman, M. Ryvkin, and M. B. Fuchs, "Nucleation of cracks in two-dimensional periodic cellular materials", Comput. Mech. 39:2 (2007), 127-139.
12. F. Lipperman, M. B. Fuchs, and M. Ryvkin, "Stress localization and strength optimization of frame material with periodic microstructure", Comput. Methods Appl. Mech. Eng. 197:45-48 (2008), 4016-4026.
13. F. Lipperman, M. Ryvkin, and M. B. Fuchs, "Crack arresting low-density porous materials with periodic microstructure", Int. J. Eng. Sci. 46:6 (2008), 572-584.
14. S. K. Maiti, M. F. Ashby, and L. J. Gibson, "Fracture toughness of brittle cellular solids", Scr. Metall. 18:3 (1984), 213-217.
15. K. I. Majid, M. P. Saka, and T. Celik, "The theorems of structural variation generalized for rigidly jointed frames", Proc. Inst. Civ. Eng. 65:4 Part 2 (1978), 839-856.
16. J. C. Michel, H. Moulinec, and P. Suquet, "Effective properties of composite materials with periodic microstructure: a computational approach", Comput. Methods Appl. Mech. Eng. 172:1-4 (1999), 109-143.
17. B. Nuller and M. Ryvkin, "On boundary value problems for elastic domains of a periodic structure deformed by arbitrary loads", Proc. State Hydraulic Inst. 136 (1980), 49-55. In Russian.
18. I. Quintana Alonso and N. A. Fleck, "Damage tolerance of an elastic-brittle diamond-celled honeycomb", Scr. Mater. 56:8 (2007), 693-696.
19. M. Ryvkin and B. Nuller, "Solution of quasi-periodic fracture problems by the representative cell method", Comput. Mech. 20:1-2 (1997), 145-149.
20. M. Ryvkin, M. B. Fuchs, and B. Nuller, "Optimal design of infinite repetitive structures", Struct. Multidis-cip. O. 18:2-3 (1999), 202-209.
21. I. Schmidt and N. A. Fleck, "Ductile fracture of two-dimensional cellular structures", Int. J. Fract. 111:4 (2001), 327-342.
22. W. E. Warren and A. M. Kraynik, "Foam mechanics: the linear elastic response of two-dimensional spatially periodic cellular materials", Mech. Mater. 6:1 (1987), 27-37.
23. W. E. Warren and A. M. Kraynik, "The linear elastic properties of open-cell foams", J. Appl. Mech. (ASME) 55 (1988), 341-346.