A parametric model for foam-like materials is proposed and its correlation with experimental results is analyzed. The class of foam-like materials is assumed to be described by an isotropic elastic potential based on a general model proposed by Ogden. The class is parametrized using the relative mass density of the material. Functional relations between material parameters and the relative mass density are obtained from experimental data. A simple application problem, namely the optimization of a foam for maximum energy absorption under homogeneous compression, is formulated and solved numerically. [S0021-8936(00)02802-6]
Issue Section:
Technical Papers
1.
Ashby
, M. F.
, 1983
, “The Mechanical Properties of Cellular Solids
,” Metall. Trans. A
, 14A
, pp. 1755
–1769
.2.
Maiti
, S. K.
, Gibson
, L. J.
, and Ashby
, M. F.
, 1984
, “Deformation and Energy Absorption Diagrams for Cellular Solids
,” Acta Metall.
, 32
, No. 11
, pp. 1963
–1975
.3.
Gibson, L. J., and Ashby, M. F., 1997, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, UK.
4.
Blatz
, P. J.
, and Ko
, W. L.
, 1962
, “Application of Finite Elastic Theory to the Deformation of Rubbery Materials
,” Trans. Soc. Rheol.
, VI
, pp. 223
–251
.5.
Ogden
, R. W.
, 1972
, “Large Deformation Isotropic Elasticity: On the Correlation of Theory and Experiment for Compressible Rubberlike Solids
,” Proc. R. Soc. London, Ser. A
, 328
, pp. 567
–583
.6.
Ball
, J. M.
, 1977
, “Convexity Conditions and Existence Theorems in Nonlinear Elasticity
,” Arch. Ration. Mech. Anal.
, 63
, pp. 337
–403
.7.
Dacorogna, B., 1989, Direct Methods in the Calculus of Variations, Springer-Verlag, New York.
8.
Ball
, J. M.
, and Murat
, F.
, 1984
, “W1,p-quasiconvexity and Variational Problems for Multiple Integrals
,” J. Funct. Anal.
, 58
, pp. 225
–253
.9.
Horgan
, C. O.
, 1996
, “Remarks on Ellipticity for the Generalized Blatz-Ko Constitutive Model for a Compressible Nonlinearly Elastic Solid
,” J. Elast.
, 42
, pp. 165
–176
.10.
Warren
, W. E.
, and Kraynik
, A. M.
, 1997
, “Linear Elastic Behavior of a Low-Density Kelvin Foam With Open Cells
,” ASME J. Appl. Mech.
, 64
, pp. 787
–794
.11.
El-Ratal
, W. H.
, and Mallick
, P. K.
, 1996
, “Elastic Response of Flexible Polyurethane Foams in Uniaxial Tension
,” J. Eng. Mater. Technol.
, 118
, pp. 157
–161
.12.
Twizell
, E. H.
, and Ogden
, R. W.
, 1983
, “Nonlinear Optimization of the Material Constants in Ogden’s Stress-Deformation Function for Incompressible Isotropic Elastic Materials
,” J. Aust. Math. Soc. B, Appl. Math.
, 24
, pp. 424
–434
.13.
Lakes
, R.
, Rosakis
, P.
, and Ruina
, A.
, 1993
, “Microbuckling Instability in Elastomeric Cellular Solids
,” J. Mater. Sci.
, 28
, No. 17
, pp. 4667
–4672
.14.
Abeyaratne
, R.
, and Triantafyllidis
, N.
, 1984
, “An Investigation of Localization in a Porous Elastic Material Using Homogenization Theory
,” ASME J. Appl. Mech.
, 51
, No. 3
, pp. 481
–486
.15.
Bendso̸e
, M. P.
, Guedes
, J. M.
, Haber
, R. B.
, Pedersen
, P.
, and Taylor
, J. E.
, 1994
, “An Analytical Model to Predict Optimal Properties in the Context of Optimal Structural Design
,” ASME J. Appl. Mech.
, 61
, pp. 930
–937
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