Apparent and effective physical properties of heterogeneous materials: Representativity of samples of two materials from food industry

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 33-36, 2006, Pages 3960-3982

  Kanit, Toufik ^a   N'Guyen, Franck ^a   Forest, Samuel ^a   Jeulin, Dominique ^a   Reed, Matt ^b   Singleton, Scott ^b  

^a PSL RESEARCH UNIVERSITY   (France)

^b UNILEVER RESEARCH   (United Kingdom)

Author keywords

Elasticity; Finite element; Food material; Homogenization; Ice cream; Parallel computing; Percolation; Representative volume element; Thermal conductivity

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT METHOD; IMAGE ANALYSIS; PARALLEL PROCESSING SYSTEMS; THERMAL CONDUCTIVITY;

HOMOGENIZATION; ICE CREAM; REPRESENTATIVE VOLUME ELEMENT;

FOOD PRODUCTS;

BOUNDARY CONDITIONS; COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT METHOD; FOOD PRODUCTS; IMAGE ANALYSIS; PARALLEL PROCESSING SYSTEMS; THERMAL CONDUCTIVITY;

EID: 33747887299     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.07.022     Document Type: Article

References (44)

1. Adler P., Jacquin C., and Quiblier J. Flow in simulated porous media. Int. J. Multiphase Flow 16 (1990) 691-712
2. Adler P., Jacquin C., and Thovert J.-F. The formation factor of reconstructed model three-dimensional porous media. Water Resour. Res. 28 (1992) 1571-1576
3. Barbe F., Decker L., Jeulin D., and Cailletaud G. Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model. Int. J. Plast. 17 (2001) 513-536
4. Bergman D. The dielectric constant of a composite material, a problem in classical physics. Phys. Rep. 43 (1978) 377-407
5. Besson J., Cailletaud G., Chaboche J.L., and Forest S. Mécanique non linéaire des matériaux (2001), Hermès Science
6. Bron F., and Jeulin D. Modeling a food microstructure by random sets. Image Anal. Stereol. 23 (2004) 33-44
7. Cailletaud G., Forest S., Jeulin D., Feyel F., Galliet I., Mounoury V., and Quilici S. Some elements of microstructural mechanics. Comput. Mater. Sci. 27 (2003) 351-374
8. Cailletaud G., Jeulin D., and Rolland P. Size effect on elastic properties of random composites. Engrg. Comput. 11 (1994) 99-110
9. U.R. Colworth, Unilever Laboratory Progress Report, Unilever Research Colworth, 2000.
10. Elvin A. Number of grains required to homogenize elastic properties of polycrystalline ice. Mech. Mater. 22 (1996) 51-64
11. 2 multiscale approach for the modelling of the elastoviscoplastic behavior of long fibre SiC/Ti composites materials. Comput. Methods Appl. Mech. Engrg. 183 (2000) 309-330
12. Flannery B., Deckman H., Roberts W., and Damico K. Three-dimensional X-ray microtomography. Science 237 (1987) 1439
13. Fredrich J., Menendez B., and Wong T. Imaging the pore structure of geomaterials. Science 268 (1995) 276-279
14. Garboczi E., and Day A. An algorithm for computing the effective linear elastic properties of heterogeneous materials; three-dimensional results for composites with equal phase Poisson ratios. J. Mech. Phys. Solids 43 (1995) 1349-1362
15. Hashin Z. Analysis of composite materials. J. Appl. Mech. 50 (1983) 481-505
16. Hazanov S., and Huet C. Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume. J. Mech. Phys. Solids 42 (1994) 1995-2011
17. Huet C. Application of variational concepts to size effects in elastic heterogeneous bodies. J. Mech. Phys. Solids 38 (1990) 813-841
18. C. Huet, Hierarchies and bounds for size effects in heterogeneous bodies. In: G. Maugin (Ed.), Proceedings of the Sixth Symposium on Continuum Moels and Discrete Systems, Dijon, 1989, vol. 2, 1991, pp. 127-134.
19. Janssen P. Modelling fat microstructures using finite element analysis. J. Food Engrg. 61 (2004) 387-392
20. Jeulin D., and Ostoja-Starzewski M. Mechanics of Random and Multiscale Microstructures (2001), Springer
21. Kanit T., Forest S., Mounoury V., and Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40 (2003) 3647-3679
22. Kouznetsova V. Computational Homogenization for the Multi-Scale Analysis of Multi-Phase Materials (2002), Technische Universiteit Eindhoven
23. Kwiecien M., Macdonald I., and Dullien F. Three-dimensional reconstruction of porous sandstone from serial section data. J. Microsc. 159 (1990) 343-359
24. Leßle P., Dong M., Soppa E., and Schmauder S. Simulation of interpenetrating microstructures by self-consistent matricity models. Scripta Mater. 38 9 (1998) 1327-1332
25. Lippmann N., Steinkopf T., Schmauder S., and Gumbsch P. 3D-finite-element-modelling of microstructures with the method of multiphase elements. Comput. Mater. Sci. 9 (1997) 28-35
26. Maire E., Fazékas A., Salvo L., Dendievel R., Souhail Y., Cloetens P., and Letang J. X-ray tomography applied to the characterization of cellular materials: related finite element modeling problems. Compos. Sci. Technol. 63 (2003) 2431-2443
27. Matheron G. The Theory of Regionalized Variables and its Applications (1971), Paris School of Mines Publications
28. Ostoja-Starzewski M. Random field models of heterogeneous materials. Int. J. Solids Struct. 35 19 (1998) 2429-2455
29. Poutet J., Manzoni D., Hage-chehade F., Jacquin C., Bouteca M., Thovert J., and Adler P. The effective mechanical properties of random porous media. J. Mech. Phys. Solids 44 (1996) 1587-1620
30. Roberts A., and Teubner M. Transport properties of heterogeneous materials derived from Gaussian random fields: bounds and simulation. Phys. Rev. E51 (1995) 4141-4154
31. Sab K. On the homogenization and the simulation of random materials. Eur. J. Mech. Solids 11 (1992) 585-607
32. Sab K., and Nedjar B. Periodization of random media and representative volume element size for linear composites. C.R. Mécanique 333 (2005) 187-195
33. Sahimi M. Flow, dispersion, and displacement processes in porous media and fractured rocks: From continuum models to fractals, percolation, cellular automata and simulated annealing. Rev. Mod. Phys. 65 (1993) 1393-1534
34. Sanchez-Palencia E., and Zaoui A. Homogenization Techniques for Composite Media. Lecture Notes in Physics No. 272 (1987), Springer, Berlin
35. S. Schmauder, U. Weber, I. Hofinger, A. Neubrand, Modelling the deformation behaviour of W/Cu composites by a self-consistent matricity model, Technische Mechanik, Band 19, Heft 4, 1999, pp. 313-320.
36. Schwartz L., Auzerais F., Dunsmuir J., Martys N., Bentz D., and Torquato S. Transport and diffusion in three dimensional composite media. Physica, A 207 (1993) 28-36
37. Spanne P., Thovert J., Jacquin J., Lindquist W., Jones K., and Coker D. Synchotron computed microtomography of porous media: topology and transport. Phys. Rev. Lett. 73 (1994) 2001-2004
38. Terada K., Hori M., Kyoya T., and Kikuchi N. Simulation of the multi-scale convergence in computational homogenization approaches. Int. J. Solids Struct. 37 (2000) 2285-2311
39. Torquato S. Random heterogeneous media: microstructure and improved bounds on effective properties. Appl. Mech. Rev. 44 (1991) 37-76
40. Torquato S. Random Heterogeneous Materials (2002), Springer
41. Zohdi T. Computational optimization of the vortex manufacturing of advanced materials. Comput. Methods Appl. Mech. Engrg. 190 (2001) 6231-6256
42. Zohdi T. Constrained inverse formulations in random material design. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3179-3194
43. Zohdi T., and Wriggers P. Aspects of the computational testing of the mechanical properties of microheterogeneous material samples. Int. J. Numer. Methods. Engrg. 50 (2001) 2573-2599
44. Zohdi T., Wriggers P., and Huet C. A method of substructuring large-scale computational micromechanical problems. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5639-5656