326
S. Ghosh et al.
References
1. R. Hill, Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys.
Solids 11, 357–372 (1963)
2. Z. Hashin, S. Shtrikman, A variational approach to the theory of the elastic behaviour of
multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)
3. M. Stroeven, H. Askes, L.J. Sluys, Numerical determination of representative volumes for
granular materials. Comput. Methods Appl. Mech. Eng. 193(30–32), 3221–3238 (2004)
4. M. Thomas, N. Boyard, L. Perez, Y. Jarny, D. Delaunay, Representative volume element of
anisotropic unidirectional carbon-epoxy composite with high-fibre volume fraction. Compos.
Sci. Technol. 68(15–16), 3184–3192 (2008)
5. C. Heinrich, M. Aldridge, A.S. Wineman, J. Kieffer, A.M. Waas, K. Shahwan, The influence
of the representative volume element (RVE) size on the homogenized response of cured fiber
composites. Model. Simul. Mater. Sci. Eng. 20(7), 075007 (2012)
6. R. Hill, The essential structure of constitutive laws for metal composites and polycrystals. J.
Mech. Phys. Solids 15, 79–95 (1967)
7. H.J. Böhm, A short introduction to continuum micromechanics, in Mechanics of Microstructured Materials: CISM Courses and Lectures, ed. by H.J. Böhm, vol. 464 (Springer, Wien,
2004), pp. 1–40
8. P.W. Chung, K.K. Tamma, R.R. Namburu, A finite element thermo-viscoelastic creep for
heterogeneous structures with dissipative correctors. Finite Elem. Anal. Des. 36, 279–313
(2000)
9. S. Ghosh, Micromechanical Analysis and Multi-scale Modeling Using the Voronoi Cell Finite
Element Method (CRC Press/Taylor & Francis, Boca Raton, 2011)
10. N. Willoughby, W.J. Parnell, A.L. Hazel, I.D. Abrahams, Homogenization methods to approximate the effective response of random fibre-reinforced composites. Int. J. Solids Struct. 49(13),
1421–1433 (2012)
11. J. Fish, K. Shek, Multiscale analysis of composite materials and structures. Compos. Sci.
Technol. 60, 2547–2556 (2000)
12. S. Ghosh, K. Lee, S. Moorthy, Multiple scale analysis of heterogeneous elastic structures using
homogenization theory and Voronoi cell finite element method. Int. J. Solids Struct. 32(1),
27–62 (1995)
13. S. Ghosh, K. Lee, S. Moorthy, Two scale analysis of heterogeneous elastic-plastic materials
with asymptotic homogenization and Voronoi cell finite element model. Comput. Methods
Appl. Mech. Eng. 132(1–2), 63–116 (1996)
14. J.M. Guedes, N. Kikuchi, Preprocessing and postprocessing for materials based on the
homogenization method with adaptive finite element methods. Comput. Methods Appl. Mech.
Eng. 83, 143–198 (1991)
15. V. Kouznetsova, M.G.D. Geers, W.A.M. Brekelmans, Multi-scale constitutive modelling of
heterogeneous materials with a gradient-enhanced computational homogenization scheme. Int.
J. Numer. Methods Eng. 54, 1235–1260 (2002)
16. K. Terada, N. Kikuchi, Simulation of the multi-scale convergence in computational homogenization approaches. Int. J. Solids Struct. 37, 2285–2311 (2000)
17. F. Feyel, J.H. Chaboche, FE
2 multiscale approach for modelling the elastoviscoplastic
behaviour of long fibre SiC/Ti composite materials. Comput. Methods Appl. Mech. Eng. 183,
309–330 (2000)
18. S. Swaminathan, S. Ghosh, N.J. Pagano, Statistically equivalent representative volume elements for unidirectional composite microstructures: part I-without damage. J. Compos. Mater.
40(7), 583–604 (2006)
19. S. Swaminathan, N.J. Pagano, S. Ghosh, Statistically equivalent representative volume elements for unidirectional composite microstructures: part II-with interfacial debonding. J.
Compos. Mater. 40(7), 605–621 (2006)
S. Ghosh et al.
References
1. R. Hill, Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys.
Solids 11, 357–372 (1963)
2. Z. Hashin, S. Shtrikman, A variational approach to the theory of the elastic behaviour of
multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)
3. M. Stroeven, H. Askes, L.J. Sluys, Numerical determination of representative volumes for
granular materials. Comput. Methods Appl. Mech. Eng. 193(30–32), 3221–3238 (2004)
4. M. Thomas, N. Boyard, L. Perez, Y. Jarny, D. Delaunay, Representative volume element of
anisotropic unidirectional carbon-epoxy composite with high-fibre volume fraction. Compos.
Sci. Technol. 68(15–16), 3184–3192 (2008)
5. C. Heinrich, M. Aldridge, A.S. Wineman, J. Kieffer, A.M. Waas, K. Shahwan, The influence
of the representative volume element (RVE) size on the homogenized response of cured fiber
composites. Model. Simul. Mater. Sci. Eng. 20(7), 075007 (2012)
6. R. Hill, The essential structure of constitutive laws for metal composites and polycrystals. J.
Mech. Phys. Solids 15, 79–95 (1967)
7. H.J. Böhm, A short introduction to continuum micromechanics, in Mechanics of Microstructured Materials: CISM Courses and Lectures, ed. by H.J. Böhm, vol. 464 (Springer, Wien,
2004), pp. 1–40
8. P.W. Chung, K.K. Tamma, R.R. Namburu, A finite element thermo-viscoelastic creep for
heterogeneous structures with dissipative correctors. Finite Elem. Anal. Des. 36, 279–313
(2000)
9. S. Ghosh, Micromechanical Analysis and Multi-scale Modeling Using the Voronoi Cell Finite
Element Method (CRC Press/Taylor & Francis, Boca Raton, 2011)
10. N. Willoughby, W.J. Parnell, A.L. Hazel, I.D. Abrahams, Homogenization methods to approximate the effective response of random fibre-reinforced composites. Int. J. Solids Struct. 49(13),
1421–1433 (2012)
11. J. Fish, K. Shek, Multiscale analysis of composite materials and structures. Compos. Sci.
Technol. 60, 2547–2556 (2000)
12. S. Ghosh, K. Lee, S. Moorthy, Multiple scale analysis of heterogeneous elastic structures using
homogenization theory and Voronoi cell finite element method. Int. J. Solids Struct. 32(1),
27–62 (1995)
13. S. Ghosh, K. Lee, S. Moorthy, Two scale analysis of heterogeneous elastic-plastic materials
with asymptotic homogenization and Voronoi cell finite element model. Comput. Methods
Appl. Mech. Eng. 132(1–2), 63–116 (1996)
14. J.M. Guedes, N. Kikuchi, Preprocessing and postprocessing for materials based on the
homogenization method with adaptive finite element methods. Comput. Methods Appl. Mech.
Eng. 83, 143–198 (1991)
15. V. Kouznetsova, M.G.D. Geers, W.A.M. Brekelmans, Multi-scale constitutive modelling of
heterogeneous materials with a gradient-enhanced computational homogenization scheme. Int.
J. Numer. Methods Eng. 54, 1235–1260 (2002)
16. K. Terada, N. Kikuchi, Simulation of the multi-scale convergence in computational homogenization approaches. Int. J. Solids Struct. 37, 2285–2311 (2000)
17. F. Feyel, J.H. Chaboche, FE
2 multiscale approach for modelling the elastoviscoplastic
behaviour of long fibre SiC/Ti composite materials. Comput. Methods Appl. Mech. Eng. 183,
309–330 (2000)
18. S. Swaminathan, S. Ghosh, N.J. Pagano, Statistically equivalent representative volume elements for unidirectional composite microstructures: part I-without damage. J. Compos. Mater.
40(7), 583–604 (2006)
19. S. Swaminathan, N.J. Pagano, S. Ghosh, Statistically equivalent representative volume elements for unidirectional composite microstructures: part II-with interfacial debonding. J.
Compos. Mater. 40(7), 605–621 (2006)