Non linear constitutive models for lattice materials

Journal of the Mechanics and Physics of Solids

Volumn 64, Issue 1, 2014, Pages 44-60

  Vigliotti, Andrea ^a   Deshpande, Vikram S ^b   Pasini, Damiano ^a  

^a MCGILL UNIVERSITY   (Canada)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Lattice materials; Multiscale mechanics; Non linear mechanics; Periodic cellular materials

Indexed keywords

COMPUTATIONAL HOMOGENISATION; LATTICE MATERIALS; MULTI-SCALE MECHANICS; NONLINEAR MECHANICS; PERIODIC BOUNDARY CONDITIONS; PERIODIC CELLULAR MATERIALS; REPRESENTATIVE VOLUME ELEMENT (RVE); STRESS-STRAIN RELATIONSHIPS;

STRESS-STRAIN CURVES;

CONSTITUTIVE MODELS;

EID: 84893764420     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2013.10.015     Document Type: Article

References (50)

1. M.F. Ashby Materials Selection in Mechanical Design 2005 Elsevier
2. J. Banhart Manufacture, characterisation and application of cellular metals and metal foams Progr. Mater. Sci. 46 6 2001 559-U3
3. B. Bidanda, and P. Bartolo Virtual Prototyping & Bio Manufacturing in Medical Applications 2008 Springer US
4. A. Braides Homogenization of some almost periodic coercive functional Rend. Accad. Naz. Sci. XL Mem. Mat. 5 9 1985 313 321
5. N. Charalambakis Homogenization techniques and micromechanics. A survey and perspectives Appl. Mech. Rev. 63 3 2010 1 10
6. M.A. Crisfield A fast incremental-iterative solution procedure that handles snap-through Comput. Struct. 13 1-3 1981 55 62 (Pubitemid 11504717)
7. M.A. Crisfield Non-Linear Finite Element Analysis of Solids and Structures vol. 2 1998 Wiley
8. V.S. Deshpande, M.F. Ashby, and N.A. Fleck Foam topology bending versus stretching dominated architectures Acta Mater. 49 6 2001 1035 1040 (Pubitemid 32284694)
9. M.S.A. Elsayed, and D. Pasini Analysis of the elastostatic specific stiffness of 2D stretching-dominated lattice materials Mech. Mater. 42 7 2010 709 725
10. M.S.A. Elsayed, and D. Pasini Multiscale structural design of columns made of regular octet-truss lattice material Int. J. Solids Struct. 47 14-15 2010 1764 1774
11. J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 241 1226 1957 376 396
12. J. Fish, and A. Wagiman Multiscale finite element method for a locally nonperiodic heterogeneous medium Comput. Mech. 12 3 1993 164 180 (Pubitemid 23709902)
13. N.A. Fleck, V.S. Deshpande, and M.F. Ashby Micro-architectured materials past, present and future Proc. R. Soc. A Math. Phys. Eng. Sci. 466 2121 2010 2495 2516
14. L.J. Gibson, and M.F. Ashby The mechanics of 3-dimensional cellular materials Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 382 1782 1982 43
15. L.J. Gibson, and M.F. Ashby Cellular Solids Structure and Properties 1999 Cambridge University Press
16. L.J. Gibson, M.F. Ashby, G.S. Schajer, and C.I. Robertson The mechanics of two-dimensional cellular materials Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 382 1782 1982 25 42
17. I.M. Gitman, H. Askes, and L.J. Sluys Representative volume existence and size determination Eng. Fract. Mech. 74 16 2007 2518 2534 (Pubitemid 47177169)
18. S. Gonella, and M. Ruzzene Homogenization and equivalent in-plane properties of two-dimensional periodic lattices Int. J. Solids Struct. 45 10 2008 2897 2915
19. L. Gong, S. Kyriakides, and N. Triantafyllidis On the stability of kelvin cell foams under compressive loads J. Mech. Phys. Solids 53 4 2005 771 794 (Pubitemid 40245174)
20. S. Graham, and N. Yang Representative volumes of materials based on microstructural statistics Scripta Mater. 48 3 2003 269 274 (Pubitemid 35432773)
21. A.A. Gusev Representative volume element size for elastic composites a numerical study J. Mech. Phys. Solids 45 9 1997 1449 1459 (Pubitemid 127412533)
22. R.G. Hutchinson, and N.A. Fleck The structural performance of the periodic truss J. Mech. Phys. Solids 54 4 2006 756 782 (Pubitemid 43121437)
23. T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin Determination of the size of the representative volume element for random composites statistical and numerical approach Int. J. Solids Struct. 40 13-14 2003 3647 3679 (Pubitemid 36659117)
24. V. Kouznetsova, W.A.M. Brekelmans, and F.P.T. Baaijens An approach to micro-macro modeling of heterogeneous materials Comput. Mech. 27 1 2001 37 48 (Pubitemid 32251829)
25. V. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme Int. J. Numer. Methods Eng. 54 8 2002 1235 1260 (Pubitemid 34724730)
26. V.G. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans Multi-scale second-order computational homogenization of multi-phase materials a nested finite element solution strategy Comput. Methods Appl. Mech. Eng. 193 48-51 2004 5525 5550 (Pubitemid 39499845)
27. R.S. Kumar, and D.L. McDowell Generalized continuum modeling of 2-D periodic cellular solids Int. J. Solids Struct. 41 26 2004 7399 7422
28. R.S. Langley The response of two-dimensional periodic structures to point harmonic forcing J. Sound Vibrat. 197 4 1996 447 469 (Pubitemid 126393323)
29. K. Matsui, K. Terada, and K. Yuge Two-scale finite element analysis of heterogeneous solids with periodic microstructures Comput. Struct. 82 7-8 2004 593 606
30. D. Mohr Mechanism-based multi-surface plasticity model for ideal truss lattice materials Int. J. Solids Struct. 42 11-12 2005 3235 3260 (Pubitemid 40200626)
31. S. Müller Homogenization of nonconvex integral functionals and cellular elastic materials Arch. Rational Mech. Anal. 99 3 1987 189 212
32. A. Needleman Material rate dependence and mesh sensitivity in localization problems Comput. Meth. Appl. Mech. Eng. 67 1 1988 69 85 (Pubitemid 18574390)
33. N. Ohno, D. Okumura, and H. Noguchi Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation J. Mech. Phys. Solids 50 5 2002 1125 1153 (Pubitemid 34247631)
34. S.D. Papka, and S. Kyriakides In-plane biaxial crushing of honeycombs - Part II analysis Int. J. Solids Struct. 36 29 1999 4397 4423
35. M.J. Pindera, H. Khatam, A.S. Drago, and Y. Bansal Micromechanics of spatially uniform heterogeneous media a critical review and emerging approaches Composites B Eng. 40 5 2009 349 378
36. D.A. Ramirez, L.E. Murr, S.J. Li, Y.X. Tian, E. Martinez, J.L. Martinez, B.I. Machado, S.M. Gaytan, F. Medina, and R.B. Wicker Open-cellular copper structures fabricated by additive manufacturing using electron beam melting Mater. Sci. Eng. A 528 16-17 2011 5379 5386
37. T.A. Schaedler, A.J. Jacobsen, A. Torrents, A.E. Sorensen, J. Lian, J.R. Greer, L. Valdevit, and W.B. Carter Ultralight metallic microlattices Science 334 6058 2011 962 965
38. R.J.M. Smit, W.A.M. Brekelmans, and H.E.H. Meijer Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling Comput. Methods Appl. Mech. Eng. 155 1-2 1998 181 192 (Pubitemid 128398118)
39. A. Spadoni, and M. Ruzzene Static aeroelastic response of chiral-core airfoils J. Intell. Mater. Syst. Struct. 18 10 2007 1067 1075 (Pubitemid 47438504)
40. M. Stroeven, H. Askes, and L.J. Sluys Numerical determination of representative volumes for granular materials Comput. Methods Appl. Mech. Eng. 193 30-32 2004 3221 3238 (Pubitemid 38791057)
41. A.S.J. Suiker, A.V. Metrikine, and R. de Borst Comparison of wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models Int. J. Solids Struct. 38 9 2001 1563 1583 (Pubitemid 32071296)
42. K. Terada, M. Hori, T. Kyoya, and N. Kikuchi Simulation of the multi-scale convergence in computational homogenization approaches Int. J. Solids Struct. 37 16 2000 2285 2311 (Pubitemid 32213460)
43. N. Triantafyllidis, and M. Schraad Onset of failure in aluminum honeycombs under general in-plane loading J. Mech. Phys. Solids 46 6 1998 1089 1124 (Pubitemid 128378400)
44. O. Van Der Sluis, P.J.G. Schreurs, W.A.M. Brekelmans, and H.E.H. Meijer Overall behaviour of heterogeneous elastoviscoplastic materials effect of microstructural modelling Mech. Mater. 32 8 2000 449 462
45. A. Vigliotti, and D. Pasini Linear multiscale analysis and finite element validation of stretching and bending dominated lattice materials Mech. Mater. 46 2012 57 68
46. A. Vigliotti, and D. Pasini Stiffness and strength of tridimensional periodic lattices Comput. Methods Appl. Mech. Eng. 2012
47. A.J. Wang, and D.L. McDowell In-plane stiffness and yield strength of periodic metal honeycombs J. Eng. Mater. Technol. Trans. ASME 126 2 2004 137 156 (Pubitemid 40122747)
48. J. Wang, A. Nausieda, S.L.D.E. Lucato, and A.G. Evans Twisting of a high authority morphing structure Int. J. Solids Struct. 44 9 2007 3076 3099 (Pubitemid 46386016)
49. J. Zhang, and M.F. Ashby Buckling of honeycombs under inplane biaxial stresses Int. J. Mech. Sci. 34 6 1992 491
50. H.X. Zhu, J.F. Knott, and N.J. Mills Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells J. Mech. Phys. Solids 45 3 1997 319