Modelling the mechanical behavior of cellular materials

Abstract Materials with a cellular structure are widespread; they include natural materials such as wood and cork as well as man-made honeycombs and foams. Their cellular structure gives rise to unique properties which can be exploited in engineering design. The selection of a specific honeycomb or foam for a particular engineering application is guided by models which describe their mechanical behavior in terms of the cell geometry and the mechanisms of deformation and failure. In this review, models for the mechanical behavior of cellular materials are first described and then used to select the optimum foam for two engineering applications, the design of packaging and of light-weight structural sandwich panels.

[1]  M. B. Rhodes,et al.  Mechanical properties of particulate‐filled polyurethane foams , 1978 .

[2]  Denis Weaire,et al.  Some remarks on the arrangement of grains in a polycrystal , 1974 .

[3]  C. Fowlkes.  Fracture toughness tests of a rigid polyurethane foam , 1974 .

[4]  Norio Sato,et al.  Mechanism of high energy absorption by foamed materials-foamed rigid polyurethane and foamed glass , 1984 .

[5]  R. Lakes.  Foam Structures with a Negative Poisson's Ratio , 1987, Science.

[6]  G. Menges,et al.  Estimation of mechanical properties for rigid polyurethane foams , 1975 .

[7]  D. R. Moore,et al.  The Deformational Behaviour of Foamed Thermoplastics , 1974 .

[8]  S. K. Maiti,et al.  Fracture toughness of brittle cellular solids , 1984 .

[9]  D. A Aboav,et al.  The arrangement of grains in a polycrystal , 1970 .

[10]  M. Zaslawsky.  Multiaxial-stress studies on rigid polyurethane foam , 1973 .

[11]  D. A. Aboav,et al.  The arrangement of cells in a net , 1980 .

[12]  Lorna J. Gibson,et al.  Failure mode maps for foam core sandwich beams , 1987 .

[13]  J. Plateau,et al.  Statique expérimentale et théorique des liquides soumis aux seules forces moléculaires , 1873 .

[14]  Alan N. Gent,et al.  Mechanics of Foamed Elastic Materials , 1963 .

[15]  K. C. Rusch.  Impact Energy Absorption by Foamed Polymers , 1971 .

[16]  K. C. Rusch.  Load-compression behavior of brittle foams , 1970 .

[17]  F. T. Lewis,et al.  The correlation between cell division and the shapes and sizes of prismatic cells in the epidermis of cucumis , 1928 .

[18]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[19]  F. T. Lewis.  THE GEOMETRY OF GROWTH AND CELL DIVISION IN EPITHELIAL MOSAICS , 1943 .

[20]  R. E. Jones,et al.  Air Flow Measurement and Its Relations to Cell Structure, Physical Properties, and Processibility for Flexible Urethane Foam , 1965 .

[21]  S. W. Thomson.  LXIII. On the division of space with minimum partitional area , 1887 .

[22]  Christopher L. Magee,et al.  Deformation characteristics of zinc foam , 1975 .

[23]  K. Johnson,et al.  Indentation of foamed plastics , 1975 .

[24]  W. Ko.  Deformations of Foamed Elastomers , 1965 .

[25]  A. Evans,et al.  Fracture Mechanics of Ceramics , 1986 .

[26]  M. C. Shaw,et al.  The plastic behavior of cellular materials , 1966 .

[27]  Michael F. Ashby,et al.  The mechanical properties of cellular solids , 1983 .

[28]  K. C. Rusch.  Energy‐absorbing characteristics of foamed polymers , 1970 .

[29]  N. Hilyard,et al.  Observations on the Impact Behaviour of Polyurethane Foams; I. The Polymer Matrix , 1971 .

[30]  W. E. Warren,et al.  Foam mechanics: the linear elastic response of two-dimensional spatially periodic cellular materials , 1987 .

[31]  Richard K. Traeger,et al.  Physical Properties of Rigid Polyurethane Foams , 1967 .

[32]  M. Ashby,et al.  Cellular solids: Structure & properties , 1988 .

[33]  Alan N. Gent,et al.  The deformation of foamed elastic materials , 1959 .

[34]  Michael F. Ashby,et al.  Deformation and energy absorption diagrams for cellular solids , 1984 .

[35]  Nicolas Rivier,et al.  On the correlation between sizes and shapes of cells in epithelial mosaics , 1982 .

[36]  Masao Nakamura,et al.  Mechanical Properties of Plastic Foams , 1969 .

[37]  C. L. Magee,et al.  The Deformation of aluminum foams , 1975 .

[38]  I. Burgess,et al.  A theoretical approach to the deformation of honeycomb based composite materials , 1979 .

[39]  P. Phillips,et al.  The mechanical properties of high‐density rigid polyurethane foams in compression: I. Modulus , 1974 .

[40]  W. E. Woolam.  A Study of the Dynamics of Low Energy Cushioning Materials Using Scale Models , 1968 .

[41]  N. Rivier,et al.  Statistical crystallography Structure of random cellular networks , 1985 .

[42]  J. M. Lederman.  The prediction of the tensile properties of flexible foams , 1971 .

[43]  I. Ward,et al.  The strain-rate, temperature and pressure dependence of yield of isotropic poly(methylmethacrylate) and poly(ethylene terephthalate) , 1970 .

[44]  A. Mcintyre,et al.  Fracture properties of a rigid polyurethane foam over a range of densities , 1979 .

[45]  A. W. England,et al.  Effect of Porosity on Compressibility of Glass , 1965 .

[46]  R. Bradt,et al.  Cell size effects on the strength of foamed glass , 1981 .

[47]  H. G. Allen.  Analysis and design of structural sandwich panels , 1969 .