Asymptotic homogenization model for generally orthotropic reinforcing networks in smart composite plates

Smart Materials and Structures

Volumn 15, Issue 5, 2006, Pages 1197-1210

  Georgiades, A V ^a   Kalamkarov, A L ^a   Challagulla, K S ^a  

^a DALHOUSIE UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; PIEZOELECTRICITY; PROBLEM SOLVING; THERMAL EXPANSION;

ASYMPTOTIC HOMOGENIZATION MODEL; ORTHOTROPIC REINFORCING NETWORKS; SMART COMPOSITE PLATES;

COMPOSITE MICROMECHANICS;

EID: 33748858737     PISSN: 09641726     EISSN: 1361665X     Source Type: Journal    
DOI: 10.1088/0964-1726/15/5/006     Document Type: Article

References (50)

1. Andrianov I V, Lesnichaya V A and Manevich L I 1985 Homogenization Methods in the Statics and Dynamics of Ribbed Shells (Moscow: Nauka)
2. Bakhvalov N and Panasenko G 1984 Homogenisation: Averaging Processes in Periodic Media (Netherlands: Kluwer-Academic)
3. Bensoussan A, Lions J L and Papanicolaou G 1978 Asymptotic Analysis for Periodic Structures (Amsterdam: North-Holland)
4. Bourdin B and Kohn R V 2005 Optimal low-weight microstructures Preprint 2005 http://www.math.lsu.edu/∼bourdin/Files/Bourdin-Kohn-2005b-Preprint.pdf
5. Budiansky B 1965 On the elastic moduli of some heterogeneous materials J. Mech. Phys. Solids 13 223-7
6. Caillerie D 1984 Thin elastic and periodic plates Math. Appl. Sci. 6 159-91
7. Challagulla K, Georgiades A V and Kalamkarov A L 2006 Asymptotic homogenization modeling of thin network structures Compos. Struct. at press
8. Christensen R M 1990 A critical evaluation for a class for a class of micromechanics models J. Mech. Phys. Solids 38 379-404
9. Cioranescu D and Donato P 1999 An Introduction to Homogenization (Oxford: Oxford University Press)
10. Cote F, Masson P and Mrad N 2002 Dynamic and static assessment of piezoelectric embedded composites Proc. SPIE 4701 316-25
11. Devries F, Dumontet H, Duvaut G and Lene F 1989 Homogenization and damage for composite structures Int. J. Numer. Methods Eng. 27 285-98
12. Drugan W J and Willis J R 1996 A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites J. Mech. Phys. Solids 44 497-524
13. Eshelby J D 1957 The determination of the elastic field of an ellipsoidal inclusion, and related problems Proc. R. Soc. A 241 376-96
14. Georgiades A V and Kalamkarov A L 2004 Asymptotic homogenization models for smart composite plates with rapidly varying thickness: part II-applications J. Multiscale Comput. Eng. 2 149-72
15. Georgiades A V, Kalamkarov A L and Challagulla K S 2003 Micromechanical analysis of smart composite structures with a periodic array of embedded actuators CAN/COM 2003 Ottawa Canada CD-ROM ID
16. Gibson R F 1994 Principles of Composite Material Mechanics (New York: McGraw-Hill)
17. Guedes J M and Kikuchi N 1990 Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods Comput. Methods Appl. Mech. Eng. 83 143-98
18. Hashin Z 1962 The elastic moduli of heterogeneous materials J. Appl. Mech. 29 143
19. Hashin Z 1983 Analysis of composite materials: a survey J. Appl. Mech. 50 481-505
20. Hashin Z and Rosen B W 1964 The elastic moduli of fiber-reinforced materials J. Appl. Mech. 31 223-32
21. Hashin Z and Shtrikman S 1963a A variational approach to the theory of elastic behavior of multiphase materials J. Mech. Phys. Solids 11 127-40
22. Hashin Z and Shtrikman S 1963b Conductivity of polycrystals Phys. Rev. 130 129-33
23. Hill R 1963 Elastic properties of reinforced solids J. Mech. Phys. Solids 11 357-72
24. Hill R 1965 A self-consistent mechanics of composite materials J. Mech. Phys. Solids 13 213-22
25. Jain A K and Sirkis J S 1994 Continuum damage mechanics in piezoelectric ceramics Adaptive Structures and Composite Materials: Analysis and Application ed E Garcia, H Cudney and A Dasgupta pp47-58
26. Kalamkarov A L 1987 On the determination of effective characteristics of cellular plates and shells of periodic structure Mech. Solids 22 175-9
27. Kalamkarov A L 1992 Composite and Reinforced Elements of Construction (Chichester: Wiley)
28. Kalamkarov A L and Georgiades A V 2002 Micromechanical modeling of smart composite structures Smart Mater. Struct. 11 423-34
29. Kalamkarov A L and Georgiades A V 2004 Asymptotic homogenization models for smart composite plates with rapidly varying thickness: part I-theory J. Multiscale Comput. Eng. 2 133-48
30. Kalamkarov A L and Kolpakov A G 1997 Analysis, Design and Optimization of Composite Structures (New York: Wiley)
31. Kalamkarov A L and Kolpakov A G 2001 A new asymptotic model for a composite piezoelastic plate Int. J. Solids Struct. 38 6027-44
32. Kalamkarov A L and Liu H Q 1998 A new model for a multiphase fiber-matrix composite materials Composites B 29 643-53
33. Kohn R V and Vogelius M 1984 A new model for thin plates with rapidly varying thickness Int. J. Solids Struct. 20 333-50
34. Kohn R V and Vogelius M 1985 A new model for thin plates with rapidly varying thickness, II: a convergence proof Quart. J. Appl. Math. 43 1-22
35. Kolpakov A G and Kolpakova I G 1995 Design of laminated composites possessing specified homogenized characteristics Comput. Struct. 57 599-604
36. Lewinski T and Telega J J 2000 Plates, Laminates and Shells: Asymptotic Analysis and Homogenization (Series on Advances in Mathematics for Applied Science vol 52) (Singapore: World Scientific)
37. Michel J C, Moulinec H and Suquet P 1999 Effective properties of composite materials with periodic microstructure: a computational approach Comput. Methods Appl. Mech. Eng. 172 109-43
38. Milton G W and Kohn R V 1988 Variational bounds on the effective moduli of anisotropic composites J. Mech. Phys. Solids 36 597-629
39. Mori T and Tanaka K 1973 Average stress in matrix and average energy of materials with misfitting inclusions Acta Metall. Mater. 21 571-4
40. Pshenichnov G I 1982 Theory of Thin Elastic Network Plates and Shells (Moscow: Nauka)
41. Reddy J N 1997 Mechanics of Laminated Composite Plates (New York: CRC Press)
42. Russel W B 1973 On the effective moduli of composite materials: effect of fiber length and geometry at dilute concentrations Z. Angew. Math. Phys. 24 581-600
43. Sanchez-Palencia E 1980 Non-Homogeneous Media and Vibration Theory (Lecture Notes in Physics) (Berlin: Springer)
44. Sendeckyj G P 1974 Elastic behavior of composites Composite Materials (Mechanics of Composite Materials vol 2) (NewYork: Academic)
45. Teply J L and Dvorak G J 1988 Bounds on overall instantaneous properties of elastic-plastic composites J. Mech. Phys. Solids 36 29-58
46. Torquato S 1991 Random heterogeneous media: microstructure and improved bounds on effective properties Appl. Mech. Rev. 44 37-76
47. Torquato S and Stell G 1985 Microstructure of two-phase random media J. Chem. Phys. 82 980-7
48. Vasiliev V V 1993 Mechanics of Composite Structures (Washington, DC: Taylor and Francis)
49. Vinson J R and Sierokowski R L 1986 The Behavior of Structures Composed of Composite Materials (Nijhoff, Dordrecht: Kluwer-Academic)
50. Zeman J and ejnoha M 2001 Numerical evaluation of effective elastic properties of graphite fiber tow impregnated by polymer matrix J. Mech. Phys. Solids 49 69-90