Relating cellular structure of open solid food foams to their Young's modulus: Finite element calculation

International Journal of Solids and Structures

Volumn 45, Issue 10, 2008, Pages 2881-2896

  Guessasma, S ^a   Babin, P ^a   Valle, G Della ^a   Dendievel, R ^b  

^a INRA   (France)

^b Grenoble INP Phelma   (France)

Author keywords

Finite element method; Low relative density material; Overlapping; Random sequential addition; Young's modulus

Indexed keywords

ALGORITHMS; DENSITY (SPECIFIC GRAVITY); FINITE ELEMENT METHOD; GAUSSIAN DISTRIBUTION; SIZE DISTRIBUTION;

LOW RELATIVE DENSITY MATERIAL; RANDOM SEQUENTIAL ADDITION;

ELASTIC MODULI;

EID: 40849092432     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.01.007     Document Type: Article

References (41)

1. Amon M., and Denson C.D. A study of the dynamics of foam growth: analysis of the growth of closely spaced spherical bubbles. Polymer Engineering and Science 24 (1984) 1026-1034
2. Andrews E., Sanders W.L., and Gibson J. Compressive and tensile behaviour of aluminum foams. Materials Science and Engineering A 270 2 (1999) 113-124
3. Babin P., Della Valle G., Dendievel R., Lassoued N., and Salvo L. Mechanical properties of bread crumbs from tomography based finite element simulations: mechanical behaviour of cellular solids. Journal of Materials Science 40 (2005) 5867-5873
4. Brezny R., and Green D.J. The effect of cell size on the mechanical behavior of cellular materials. Acta Metallurgica et Materialia 38 12 (1990) 2517
5. Brezny R., and Green D.J. Characterization of edge effects in cellular materials. Journal of Materials Science 25 (1990) 4571-4578
6. Chen C., Lu T.J., and Fleck N.A. Effect of imperfections on the yielding of two-dimensional foams. Journal of the Mechanics and Physics of Solids 47 11 (1999) 2235-2272
7. Clarke A.S., and Wiley J.D. Numerical simulation of the dense random packing of a binary mixture of hard spheres: amorphous metals. Physical Review B 35 (1987) 7350-7356
8. Dam C.Q., Brezny R., and Green D.J. Compressive behavior and deformation-mode map of an open cell alumina. Journal of Materials Research 5 (1990) 163-171
9. Donev A., Cisse I., Sachs D., Variano E.A., Stillinger F.H., Connelly R., Torquato S., and Chaikin P.M. Improving the Density of Jammed Disordered Packings Using Ellipsoids. Science 303 (2004) 990-993
10. Evans A.G., Hutchinson J.W., and Ashby M.F. Cellular solids. Current Opinion in Solid State and Materials Science 3 3 (1998) 288-303
11. Evans J.W. Random and cooperative sequential adsorption. Reviews of Modern Physics 65 4 (1993) 1281-1329
12. Gan M., Gopinathan N., Jia X., and Williams R.A. Predicting Packing Characteristics of Particles of Arbitrary Shapes. KONA 22 (2004) 82-93
13. Gibson L.J., and Ashby M.F. Cellular solids (1997), Pergamon Press Ltd, Cambridge
14. Grenestedt J.L. Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids. Journal of the Mechanics and Physics of Solids 46 1 (1998) 29-50
15. Grenestedt J.L., and Bassinet F. Influence of cell wall thickness variations on elastic stiffness of closed-cell cellular solids. International Journal of Mechanical Sciences 42 7 (2000) 1327-1338
16. Hagiwara H., and Green D.J. Elastic Behavior of Open-Cell Alumina. Journal of American Ceramic Society 70 (1987) 811-815
17. Jahne B. Practical handbook on image processing for scientific applications (1997), CRC Press, NY pp. 589
18. Kanit T., Forest S., Galliet I., Mounoury V., and Jeulin D. Determination of the size of the representative volume element for random composites: statistical and numerical approach. International Journal of Solids and Structures 40 (2003) 3647-3679
19. Kanit T., Guyen F.N., Forest S., Jeulin D., Reed M., and Singleton S. Apparent and effective physical properties of heterogeneous materials: Representativity of samples of two materials from food industryComput. Methods in Applied Mechanical Engineering 195 (2006) 3960-3982
20. Keetels C., vanVliet T., and Walstra P. Relationship between the sponge structure of starch bread and its mechanical properties. Journal of Cereal Science 24 (1996) 27-31
21. Lakes, R., 1995. In: Mühlhaus, H. (Ed.), Continuum models for materials with micro-structure. John Wiley, N.Y. Chapter 1, pp. 1-22.
22. Lassoued N., Babin P., Della Valle G., Devaux M.F., and Reguerre A.L. Granulometry of bread crumb grain: Contributions of 2D and 3D image analysis at different scale. Food Research International 40 (2007) 1087-1097
23. Lavalle P., Schaaf P., Ostafin M., Voegel J.-C., and Senger B. Colloidal particles, sedimentation, fluctuation, radial distribution function. Proceedings of the National Academy of Sciences of the United States of America 96 (1999) 11100-11105
24. Maire E., Fazekas A., Salvo L., Dendievel R., Youssef S., Cloetens P., and Letang J.M. X-ray tomography applied to the characterization of cellular materials. Related finite element modeling problems. Composites Science and Technology 63 (2003) 2431-2443
25. Mattfeldt T., and Stoyan D. Improved estimation of the pair correlation function of random sets. Journal of Microscopy 200 (2000) 158-173
26. Monetto I., and Drugan W.J. A micromechanics-based nonlocal constitutive equation for elastic composites containing randomly oriented spheroidal heterogeneities. Journal of the Mechanics and Physics of Solids 52 (2004) 359-393
27. Onck P.R., Andrews E.W., and Gibson L.J. Size effects in ductile cellular solids. Part I: modelling. International Journal of Mechanical Sciences 43 3 (2001) 681-699
28. Poutet J., Manzoni D., Hage-Chehade F., Thovert J.-F., and Adler P.M. The effective mechanical properties of random porous media. Journal of the Mechanics and Physics of Solids 44 10 (1996) 1587-1620
29. Quintanilla J. Measures of clustering in systems of overlapping particles. Mechanics of Materials 38 (2006) 849-858
30. Roberts A.P., and Garboczi E.J. Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia 49 2 (2001) 189-197
31. Roberts A.P., and Garboczi E.J. Elastic properties of model random three-dimensional open-cell solids. Journal of the Mechanics and Physics of Solids 50 1 (2002) 33-55
32. Russ C., and Russ J. improved implementation of a convexx segmentation algorithm. Acta Stereologica 7 (1988) 33-40
33. Russ J.C. Computer-Assisted microscopy: The measurement and analysis of images (1990), Plenum Press, NY pp. 453
34. Scanlon M.G., and Zghal M.C. Bread properties and crumb structure. Food Research International 34 10 (2001) 841-864
35. Serra J. image analysis and mathematical morphology (1982), Academic press, London
36. Sherwood J.D. Packing of spheroids in three-dimensional space by random sequential addition. Journal of Physics A: Mathematical and General 30 (1997) L839-L843
37. Silva M., and Gibson L. the effect of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids. International Journal of Mechanical Science 39 (1997) 549-563
38. Stillinger F.H., and Torquato S. Journal of Physical Chemistry B 108 (2004) 19589-19594
39. Talbot J., Schaaf P., and Tarjus G. Random sequential addition of hard spheres. Molecular Physics 72 6 (1991) 1397-1406
40. Topping B.H.V., Muylle J., Putanowicz R., and Cheng B. Finite Element Mesh Generation (2000), Saxe-Coburg Publ., Edinburgh pp. 250
41. Williams S.R., and Philipse A.P. Random packings of spheres and spherocylinders simulated by mechanical contraction. Physical Review E 67 (2003) 051301-051309