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The Mechanical Properties of Cellular Solids

M.F. ASHBY R. E Mehl Medalist

The mechanical properties (elastic, plastic, creep, and fracture) of cellular solids or foams are related to the properties of the cell wall material and to the cell geometry. The properties are well described by simple formulae. Such materials occur widely in nature and have many potential engineering applications.

FOREWORD

THISpaper was presented at a meeting convened to renew the memory of Professor Robert Franklin Mehl. It is easy to forget that the field in which we, most of us, w o r k - - t h e broad field of Materials Science-- is not very old. He was one of the great pioneers, one of the first to explore and map out the origins of structure in materials and the way it controls properties. The work described below, and, above all, the approach to it, is in the tradition of which he was one of the founders. The Institute of Metals Lecture was established in 1921, at which time the Institute of Metals Division was the only professional Division within the American Institute of Mining and Metallurgical Engineers. It has been given annually since 1922 by distinguished men from this country and abroad. Beginning in 1973 and thereafter, the person selected to deliver the lecture will be known as the "Institute of Metals Division Lecturer and R. F. Mehl Medalist" for that year. Dr. ASHBY received his B. A., M. A., and Ph. D. degrees at the University of Cambridge, England. He has been the Editor of Acta Metallurgica since 1974 and is an Honorary Research Fellow at Harvard University. Dr. Ashby has served as Chairman of the NATO Study Group on Materials Resources and was a member of the National Economic Development Council Study Group on Materials in the British Economy. He was elected a Fellow of the Royal Society in 1979 and is the recipient of the L. B. Pfeil Medal and the Rosenhain Medal of the Metals Society. A large portion of this work was done in collaboration with Dr. L.J. Gibson. Dr. Gibson is now Assistant Professor of Structural Engineering, University of British Columbia.

METALLURGICAL TRANSACTIONS A

I.

INTRODUCTION

When modem man builds large load-bearing structures, he uses dense solids: steel, concrete, glass. When nature does the same,* she generally uses cellular materials: wood, *To give an idea of the scale of some natural "structures", a large dinosaur was about the length and weight of a 25-seater aircraft; a large redwood tree is about the height of a 30-floor building (100 m) and weighs around 2500 tonnes.

bone, coral. There must be good reasons for this. It is, almost certainly, that cellular materials permit the simultaneous optimization of stiffness, strength, and overall weight in a given application. Cellular solids are nature's equivalent of the I-beam. Man-made foams are common enough, of course: cushioning, insulation, padding, packaging are all functions filled by cellular solids. Nature uses them in these ways, too: orange peel to protect the orange, cork bark to insulate the tree. But while nature