Generalized continuum modeling of 2-D periodic cellular solids

International Journal of Solids and Structures

Volumn 41, Issue 26, 2004, Pages 7399-7422

  Kumar, Rajesh S ^a   McDowell, David L ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Cellular solid; Cosserat; Discrete modeling; Finite elements; Generalized continuum; Micropolar

Indexed keywords

ABSORPTION; COMPUTER SIMULATION; ELASTIC MODULI; FINITE ELEMENT METHOD; FRACTURE TOUGHNESS; HONEYCOMB STRUCTURES; SANDWICH STRUCTURES; SHEAR DEFORMATION; STRAIN; STRESS ANALYSIS;

CELLULAR SOLIDS; COSSERAT; DISCRETE MODELING; GENERALIZED CONTINUUM; MICROPOLAR;

SOLID STATE DEVICE STRUCTURES;

EID: 4644285304     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2004.06.038     Document Type: Article

References (26)

1. ABAQUS, Inc., 2002. User's Manual, Version 6.3-1. Pawtucket, RI.
2. Adachi, T., Tomita, Y., Tanaka, M., 1998. Computational simulation of deformation behavior of 2D-lattice continuum. International Journal of Mechanical Science 40 (9), 857-866.
3. Askar, A., Cakmak, A.S., 1968. A structural model of micropolar continuum. International Journal of Engineering Science 6, 583-589.
4. Banks, C.B., Sokolowski, M., 1968. On certain two-dimensional applications of the couple stress theory. International Journal of Solids and Structures 4, 15-29.
5. Bazant, Z.P., 1971. Micropolar medium as model for buckling of grid frameworks. In: Developments in Mechanics, Proceedings of the 12th Midwestern Mechanics Conference, vol. 6. pp. 587-594.
6. Bazant, Z.P., Cedolin, L., 1991. Stability of Structures. Oxford University Press, New York pp. 129-138.
7. Bazant, Z.P., Christensen, M., 1972. Analogy between micropolar continuum and grid frameworks under initial stress. International Journal of Solids and Structures 8, 327-346.
8. Chen, J.Y., Huang, Y., Ortiz, M., 1998. Fracture analysis of cellular materials: a strain gradient model. Journal of the Mechanics and Physics of Solids 46 (5), 789-828.
9. Cochran, J.K., Lee, K.J., McDowell, D.L., Sanders, T.H., Church, B., Clark, J., Dempsey, B., Hayes, A., Hurysz, K., McCoy, T., Nadler, J., Oh, R., Seay, W., Shapiro, B., 2000. Low density monolithic honeycombs by thermal chemical processing. In: Proceedings of the 4th Conference on Aerospace Materials, Processes, and Environmental Technology, September 18-20, 2000, Huntsville, AL.
10. Cosserat, E., Cosserat, F., 1909. Théorie des Corps Déformables. Hermann, Paris.
11. Deshpande, V.S., Ashby, M.F., Fleck, N.A., 2001. Foam topology: bending versus stretching dominated architectures. Acta Materialia 49, 1035-1040.
12. Eringen, A.C., 1966. Linear theory of micropolar elasticity. Journal of Mathematics and Mechanics 15 (6), 909-923.
13. Eringen, A.C., 1968. Theory of micropolar elasticity. In: Liebowitz, H. (Ed.), Fracture - An Advanced Treatise, Vol. II: Mathematical Fundamentals. Academic Press, New York.
14. Eringen, A.C., 1999. Microcontinuum Field Theories I: Foundations and Solids. Springer, New York.
15. Evans, A.G., Hutchinson, J.W., Ashby, M.F., 1998. Multifunctionality of cellular metal systems. Progress in Materials Science 43, 171-221.
16. Evans, A.G., Hutchinson, J.W., Fleck, N.A., Ashby, M.F., Wadley, H.N.G., 2001. The topological design of multifunctional cellular metals. Progress in Materials Science 46, 309-327.
17. Gibson, L.J., Ashby, M.F., 1997. Cellular Solids, second ed. Cambridge University Press, Cambridge, UK.
18. Kaloni, P.N., Ariman, T., 1967. Stress concentration effects in micropolar elasticity. Journal of Applied Mathematics and Physics (ZAMP) 18, 136-141.
19. Kumar, R.S., McDowell, D.L., in preparation.
20. Nowacki, W., 1986. Theory of Asymmetric Elasticity. Pergamon Press, New York.
21. Perano, K.J., 1983. Application of micropolar elasticity to the finite element continuum analysis of articulated structures. Ph.D. Dissertation, University of California, Davis, USA.
22. Shames, I.H., Dym, C.L., 1985. Energy and Finite Element Methods in Structural Mechanics. Hemisphere Publishing Corporation, New York p. 200.
23. Wang, A.J., McDowell, D.L., 2004. In-plane stiffness and yield strength of periodic metal honeycombs. ASME Journal of Engineering Materials and Technology 126, 137-156.
24. Wang, A.J., McDowell, D.L., in press. Yield surfaces of various periodic metal honeycombs at intermediate relative density. International Journal of Plasticity.
25. Wang, X.L., Stronge, W.J., 1999. Micropolar theory for two-dimensional stresses in elastic honeycomb. Proceedings of the Royal Society of London A 455, 2091-2116.
26. Warren, W.E., Byskov, E., 2002. Three-fold symmetry restrictions on two-dimensional micropolar materials. European Journal of Mechanics A/Solids 21, 779-792.