Construction of micropolar continua from the asymptotic homogenization of beam lattices

Computers and Structures

Volumn 112-113, Issue , 2012, Pages 354-363

  Dos Reis, F ^a   Ganghoffer, J F ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Asymptotic expansions; Beam lattices; Discrete homogenization; Micropolar continuum; Microstructure effects

Indexed keywords

ASYMPTOTIC EXPANSION; ASYMPTOTIC HOMOGENIZATION; BEAM PROPERTIES; CENTRAL SYMMETRY; DISCRETE HOMOGENIZATION; EQUIVALENT CONTINUUM; EQUIVALENT STIFFNESS MATRIX; FINITE ELEMENT SIMULATIONS; INPUT FILES; LATTICE TOPOLOGY; MACROSCOPIC SCALE; MICROPOLAR; MICROPOLAR CONTINUUM; MICROPOLAR EFFECTS; MICROSTRUCTURE EFFECTS; PERIODIC BEAMS; SIMULATION CODE;

MICROSTRUCTURE;

ALGORITHMS;

EID: 84868191968     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2012.08.006     Document Type: Article

References (40)

1. L.J. Gibson Biomechanics of cellular solids J Biomech 38 2005 377 399 (Pubitemid 40126449)
2. C. McVeigh, F. Vernerey, W.K. Liu, and L.C. Brinson Multiresolution analysis for material design Comput Meth Appl Mech Eng 195 2006 5053 5076 (Pubitemid 43842596)
3. R.S. Lakes Experimental microelasticity of two porous solids Int J Solids Struct 22 1986 55 63 (Pubitemid 16475209)
4. W. Warren, and E. Byskov A general solution to some plane problems of micropolar elasticity Eur J Mech A/Solids 27 2008 18 27 (Pubitemid 350181487)
5. S. Liu, and W. Su Effective couple-stress continuum model of cellular solids and size effects analysis Int J Solids Struct 46 2009 2787 2799
6. A. Yoo, and I. Jasiuk Couple-stress moduli of a trabecular bone idealized as a 3d periodic cellular network J Biomech 39 2006 2241 2252 (Pubitemid 44223527)
7. R.S. Kumar, and D.L. McDowell Multifunctional design of two-dimensional cellular materials with tailored mesostructure Int J Solids Struct 46 14-15 2009 2871 2885
8. S. Gu, T.J. Lu, and A.G. Evans On the design of two-dimensional cellular metals for combined heat dissipation and structural load capacity Int J Heat Mass Transfer 44 2001 2163 2175
9. J. Fatemi, F. van Keulen, and P. Onck Generalized continuum theories: Application to stress analysis in bone Meccanica 37 2002 385 396 (Pubitemid 35393784)
10. J. Rosenberg, and R. Cimrman Microcontinuum approach in biomechanical modeling Math Comput Simulat 61 2003 249 260
11. S. Forest, and R. Sievert Nonlinear microstrain theories Int J Solids Struct 43 2006 7224 7245 (Pubitemid 44486178)
12. C.B. Hirschberger, E. Kuhl, and P. Steinmann On deformational and configurational mechanics of micromorphic hyperelasticity - theory and computation Comput Meth Appl Mech Eng 196 2007 4027 4044 (Pubitemid 47194325)
13. A. Askar, and A. Cakmak A structural model of a micropolar continuum Int J Eng Sci 6 1968 583 589
14. A.K. Noor Continuum modeling for repetitive lattice structures Appl Mech Rev 41 1988 285 296
15. Z. Bazant, and M. Christensen Analogy between micropolar continuum and grid frameworks under initial stress Int J Solids Struct 8 3 1972 327 346
16. R.S. Kumar, and D.L. McDowell Generalized continuum modeling of 2-d periodic cellular solids Int J Solids Struct 41 2004 7399 7422
17. N. Bakhvalov, and G. Panasenko Averaging processes in periodic media: mathematical problems in the mechanics of composite material 1989 Kluwer Academic
18. P.H. af Segerstad, S. Toll, and R. Larsson A micropolar theory for the finite elasticity of open-cell cellular solids Proc Roy Soc A 465 2009 843 865
19. X.L. Wang, and W.J. Strong Micropolar theory for two-dimensional stresses in elastic honeycomb Proc Roy Soc A: Lond 455 1999 2091 2116
20. W.E. Warren, and E. Byskov Three-fold symmetry restrictions on two-dimensional micropolar materials Eur J Mech A/Solids 21 2002 779 792
21. P.R. Onck Cosserat modeling of cellular solids C R Mecanique 330 2002 717 722 (Pubitemid 35408243)
22. P.-G. Martinsson, and I. Babuška Mechanics of materials with periodic truss or frame micro-structures Arch Rat Mech Anal 185 2007 201 234
23. E. Sanchez-Palencia Homogenization method for the study of composite media F. Verhulst, Asymptotic analysis II Lecture notes in mathematics vol. 985 1983 Springer Berlin/ Heidelberg 192 214
24. D. Cioranescu, and J. Paulin Homogenization of reticulated structures 1999 Springer
25. C. Boutin Microstructural effects in elastic composites Int J Solids Struct 33 7 1996 1023 1051 (Pubitemid 126403875)
26. F. Pradel, K. Sab, Cosserat modelling of elastic periodic lattice structures, Comptes Rendus de l'Académie des Sciences, Paris t. 326, Serie II b, 1998, pp. 699-704. (Pubitemid 29369318)
27. K. Sab, and F. Pradel Homogenisation of periodic cosserat media Int J Comput Appl Technol 34 2009 60 71
28. G. Moreau, and D. Caillerie Continuum modeling of lattice structures in large displacement applications to buckling analysis Comput Struct 68 1998 181 189 (Pubitemid 128423862)
29. H. Tollenaere, and D. Caillerie Continuous modeling of lattice structures by homogenization Adv Eng Software 29 1998 699 705 (Pubitemid 128369543)
30. C. Boutin, and S. Hans Homogenisation of periodic discrete medium: Application to dynamics of framed structures Comput Geotech 30 4 2003 303 320 (Pubitemid 36339705)
31. C. Boutin, S. Hans, and C. Chesnais Generalized beams and continua. dynamics of reticulated structures Mech Gen Contin 2010 131 141
32. F. Dos Reis, and J. Ganghoffer Equivalent mechanical properties of auxetic lattices from discrete homogenization Comput Mater Sci 51 1 2012 314 321
33. D. Caillerie, A. Mourad, and A. Raoult Discrete homogenization in graphene sheet modeling J Elast 84 2006 33 68 (Pubitemid 43999266)
34. E. Cosserat, F. Cosserat, Théorie des Corps Déformables, Librairie Scientifique A. Hermann et Fils, 1909.
35. R. Toupin Elastic materials with couple stresses Arch Rat Mech Anal 11 1962 385 413
36. A.C. Eringen Linear theory of micropolar elasticity J Math Mech 15 1966 909 923
37. W. Koiter Couple stresses in the theory of elasticity i,ii Proc Kon Ned Akad Wetenschap B 67 1964 17 44
38. R. Mindlin, and H. Tierstein Effects of couple stresses in linear elasticity Arch Rat Mech Anal 11 1962 415 447
39. P. Trovalusci, and R. Masiani Material symmetries of micropolar continua equivalent to lattices Int J Solids Struct 36 1999 2091 2108 (Pubitemid 129507296)
40. R. Gauthier, and W. Jashman A quest for micropolar elastic constants J Appl Mech 42 1975 369 374