PROFESSOR MARKUS REINER, Dr. Tech. Gerard Swope Professor of Mechanics, Technion—Israel Institute of Technology, Haifa. Member of The Israel Academy of the Sciences and the Humanities. Born 5 January 1886. CONTRIBUTIONS TO MECHANICS Markus Reiner Eightieth Anniversary Volume Edited by DAVID ABIR Technion - Israel Institute of Technology, Haifa <§§» PERGAMON PRESS OXFORD-LONDON-EDINBURGH-NEW YORK TORONTO · SYDNEY · PARIS · BRAUNSCHWEIG Pergamon Press Ltd., Headington Hill Hall, Oxford 4 & 5 Fitzroy Square, London W.l Pergamon Press (Scotland) Ltd., 2 & 3 Teviot Place, Edinburgh 1 Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford, New York 10523 Pergamon of Canada Ltd., 207 Queen's Quay West, Toronto 1 Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia Pergamon Press S.A.R.L., 24 rue des Écoles, Paris 5e Vieweg & Sohn GmbH, Burgplatz, 1, Braunschweig Copyright © 1969 David Abir First edition 1969 Library of Congress Catalog Card No. 68-26907 Printed in Hungary 08 012822 X PREFACE To THE numerous friends of Professor Markus Reiner it may come as a surprise to learn that he is in his eighties now (born 5 January 1886). His vitality and activity defy his age. Of the dozens of research projects conducted by Reiner, the two most important were published at the ages of 59 and 62.f In 1947, being 61 years old (the retirement age for many people from active work), he opened a new and flourishing chapter in his life as Professor of Mechanics at the Technion—Israel Institute of Tech- nology, Haifa, thus becoming an academic after almost 40 years of work as a practising civil engineer. At the age of 70 Reiner exhibited his centri- petal pump, which caused a stir and keen discussion among professional circles. Reiner continues to display vivid interest and energy in many facets of activity, both intellectual and physical; he still publishes papers and swims almost daily in the sea or pool. May he carry on his energetic and fruitful activity for many more years! The prolific and diverse contribution of Professor Reiner in the field of Mechanics in general, and Rheology in particular, is well known. It stands out not only in quality, but also in quantity. Though he spent the first four decades of his adult life as a full-time engineer, doing research as a hobby in his spare time only (apart from two years devoted solely to research), he has published to date an impressive number of publica- tions—172 papers and notes. The more significant of these, sixty-eight in number, are given in the selected list of his works, which follows this Preface. The list also includes Reiner's three fundamental books (one of them written in collaboration with Dr. G.W. Scott Blair), which were translated into several languages. Reiner's work has been recognized by numerous academic and profes- sional institutions, both in his own country, Israel (where he has been living close to half a century), and in a number of other countries. The list of awards, prizes, honorary memberships, etc., bestowed upon him by many learned societies is both lengthy and noteworthy. t (1) "A mathematical theory of dilatancy", American Journal of Mathematics 67, 350-62 (1945). (2) "Elasticity Beyond the Elastic Limit", ibid. 70, 433-46 (1948). TÜ Vlll Preface The present book, too, is a manifestation of esteem and affection to Professor Reiner, expressed by thirty-three authors from various coun- tries, who eagerly contributed original works. The number of contribu- tors might easily have been much larger; but in order to avoid too volu- minous a book, invitations for papers were confined to personal friends of Markus Reiner in the narrow professional field. Even so, it is quite likely that a good number of people who might fall within this category of friends have been left out. To these, sincerest apologies are hereby offered ; any such omission was unintentional and a result of unawareness. The papers in this volume are conveniently grouped in parts, according to their contents. This grouping, however, should not be considered as rigid ; neither should it be taken as a measure of relative merit or signifi- cance. In each part, the papers are arranged in alphabetical order of the authors. The list of contributions opens with a biographical survey of Reiner's life, written by Dr. Scott Blair—his close friend for almost four decades. In editing the volume no attempt was made to unify the style of writing of the various authors ; it was thought that the personal way of presen- tation of the individual contributors should be preserved. Some editorial changes, however, have been introduced in the manuscripts, either for the sake of clarity of the subject-matter or in accordance with English language requirements. By the same token, the spelling of words which are written differently in Great Britain and America has been left intact according to preference of the individual authors ; however, in order to avoid misunderstandings and confusion, uniformity has been adopted throughout the book in designating the serial numbers of References by square brackets, and of equations by parentheses. Finally, thanks are expressed to the authorities of the Technion-Israel Institute of Technology, Haifa, for their encouragement in the preparation of this volume; and sincere gratitude and appreciation are due to Eng. E. Goldberg, who contributed significantly as language editor for part of the material. DAVID ABIR SELECTED LIST OF PUBLICATIONS BY MARKUS REINER BOOKS 1943: Ten Lectures on Theoretical Rheology, R. Mass, Jerusalem. (Trans- lated into Russian, Moscow, 1947.) 1949: Deformation and Flow, H. K. Lewis & Co., London. (Translated into Japanese, Tokyo, 1957.) 1949 : Twelve Lectures on Theoretical Rheology (revised and enlarged edition of 1943 book), North Holland Publishing Co., Amsterdam. (Trans- lated into French, Paris, 1955; and Polish, Warsaw, 1958.) 1957: Agricultural Rheology (in collaboration with G. W. SCOTT BLAIR), Routledge & Kegan Paul, London. (Translated into Japanese, Tokyo, 1960.) 1960: Lectures on Theoretical Rheology (revised and enlarged edition of 1949 book), North Holland Publishing Co., Amsterdam. 1960: Deformation, Strain and Flow (revised and enlarged edition of 1949 book), H. K. Lewis & Co., London. (Translated into Russian, Moscow, 1963; and German, Munich, 1967.) SELECTED PAPERS 1911: Deformationswiderstand, tangentiale Kohaesion and Reibungs- widerstand von Fluessigkeiten, Zeitschrift des oesterreichischen Ingenieur- u. Architekten Vereins, 63, 803-7. 1914: Ueber die Torsionsbeanspruchung von Wellen, Zeitschr. d. oesterr. Ing. u. Arch. Ver. 18,1-6. 1915: Ueber das Auftreten von Normalspannungen bei der Torsion pris- matischer Staebe, Oesterr. Wochenschrift fuer den oeffentlichen Baudienst. 1917: Ueber die Berechnung der Auflagereibung von Tragwerken, Zeitschr. d. oesterr. Ing. u. Arch. Ver. 69, 574-6, 584-7. 1924: Structural steelwork reinforced with concrete, Concrete and Constr. £wg.l9,445. 1925: Ueber die Torsion prismatischer Staebe durch Kraefte, die auf den iz x Selected List of Publications by Markus Reiner Mantel einwirken. Zeitschrift f angewandte Mathematik u. Me- chanik, 5,409-17. 1925 : Safety of retaining walls against sliding, Concr. and Constr. Eng. 20, 183. 1926: Ueber die Stroemung einer elastischen Fluessigkeit durch eine Kapillare, Kolloid-Zeitschrift 39, 80-87. 1926: Zur Theorie der Strukturturbulenz, Kolloid-Zeitschr. 39, 314-15. 1927: (in collaboration with R. RIWLIN) Ueber die Stroemung einer elas- tischen Fluessigkeit im Couette Apparat, Kolloid-Zeitschr. 43, 1-5. 1929 : The general law of flow of matter, /. Rheology 1, 11-20. 1930: In search of a general law of flow of matter, Rheology 1, 250-60. 1930: Zur Hydrodynamik der Kolloide, Zeitschr. f angew. Math. u. Mech. 10,400-13. 1931 : Slippage in a non-Newtonian liquid, Rheology 2, 337-50. 1932: Outline of a systematic survey of rheological theories, Rheology 3,245-56. 1932: Die Berechnung des Einflusses einer festen Wand auf den Aggre- gatzustand einer Fluessigkeit aus Viskositaetsmessungen, Physika- lische Zeitschrift 33,499-502. 1933: Ueber den Gebrauch der Potenzfunktion zur Darstellung einer naturgesetzlichen Beziehung, Die Naturwissenschaften 21, 294-9. 1933: A contribution to the theory of the straight beam, Quarterly J. of Mathematics (Oxford), 4,12-20. 1933: (in collaboration with E. C. BINGHAM) The rheological properties of cement and cement mortar stone, Physics 4, 88-96. 1933: (in collaboration with R. SCHOENFELD-REINER) Viskometrische Untersuchungen hochmolekularer Naturstoffe : Kautschuk in Toluol, Kolloid Zeitschr. 65,44-62. 1934 : The theory of non-Newtonian liquids, Physics 5, 321-41. 1934 : Viscometric studies of rubber solutions, Physics 5,342-9. 1938: (in collaboration with A. FREUDENTHAL) Failure of a material showing creep (a dynamical theory of strength), Proc. 5th Intern. Congr. Appl. Mechanics. 1939: (in collaboration with K. WEISSENBERG) A thermodynamical theory of the strength of materials, Rheology Leaflet No. 10, pp. 12-20. 1945: A mathematical theory of dilatancy, Am. J. Math. 67, 350-62. 1945: (in collaboration with A. ARNSTEIN) Creep of cement and cement mortar, CivilEngineering 40,198-202. Selected List of Publications by Markus Reiner xi 1946: The coefficient of viscous traction, Am. J. Math. 68, 672-80. 1946: A simple instrument for measuring blast, /. Scientific Instruments 23, No. 12. 1948: Research on the workhardening of polycrystalline metals. Palestine Board for Scientific & Industrial Research, Jerusalem. 1948: Research on the rheological properties of bitumen and asphalt. Palestine Board for Scientific & Industrial Research, Jerusalem. 1948 : Elasticity beyond the elastic limit, Am. J. Math. 70,433-46. 1949: On volume or isotropic flow, Applied Scientific Research A. 1, 471-88. 1949: (in collaboration with G. W. SCOTT BLAIR and G. MOCQUOT) Sur un aspect de méchanisme de formation des lainures dans le fromage de Gruyère compte, Le Lait 29, 351-7. 1949: (in collaboration with G. W. SCOTT BLAIR and H. B. HAWLEY) The Weissenberg effect in sweetened condensed milk, /. Soc. Chem. Ind. 68, 327-8. 1950: The volume flow of asphalt, J. Soc. Chem. Ind. 69,257-60. 1950: (in collaboration with A. ARNAN and M. TEINOWITZ) Research on loading tests of reinforced concrete floor structures. Research Council of Israel, Jerusalem. 1951: An investigation into the rheological properties of bitumen: Maxwell body and elastic dispersions. Bull. Res. Counc. Israel 1, No. 3, 5-25. 1952: (in collaboration with I. BRAUN) Problems of cross-viscosity, Quart. J. Mech. Appl. Math. 5,42-53. 1952: (in collaboration with I. BRAUN) Note on dimensions in tensor analysis, Bull. Res. Counc. Israel 1, 81-82. 1952: A possible cross-viscosity effect in air, Bull. Res. Counc. Israel 2, 65. 1952: A tea-pot effect, Bull. Res. Counc. Israeli, 265. 1953: On volume viscosity, Proc. 8th Intern. Congr. Appl. Mechanics, Istanbul, p. 273. 1954: Volume rheology, Proc. 2nd Intern. Congr. Rheology, 1953, Butter- worths, London, pp. 310-15. 1955 : The complete elasticity law for some metals according to Poynting's observations. Appl. Sei. Res., A. 5,281-95. 1956 : The tea-pot effect, Physics Today 9,16-20. 1956: (in collaboration with M. HANIN) On isotropic tensor functions and the measure of deformation ZAMP 7, 377-93. 1956: Phenomenological macrorheology, Rheology 1 (ed. F. EIRICH), pp. 9-62, Academic Press, New York. xii Selected List of Publications by Markus Reiner 1956: (in collaboration with B. POPPER) The application of the centri- petal effect in air to the design of a pump, Brit. J. Appl. Phys. 7, 452-3. 1957: A centripetal pump effect in air, Proc. Roy. Soc. A. 240, 173-89. 1958: (in collaboration with L. RINTEL) The complete stress-strain law in infinitesimal elasticity, Bull. Res. Counc. Israel 6C 113-26. 9 1958: Rheology, Encyclopaedia of Physics 6 (ed. S. FLUEGGE), pp. 434-550, Springer-Verlag, Berlin. 1958: The centripetal-pump effect in a vacuum pump, Proc. Roy. Soc. A. 247,152-67. 1959 : The flow of matter, Scientific American 201,122-38. 1960: The rheology of concrete, Rheology 3 (ed. F. EIRICH), pp. 341-64, Academic Press, New York. 1960: Cross-stresses in the laminar flow of liquids, Physics of Fluids 3, 427-32. 1960: The stress-strain relation of elasticity and the measure of strain, ZAMM 40,415-20. 1960: Plastic yielding in anelasticity, /. Mech. Phys. Solids 8, 255-61. 1962: (in collaboration with A. Foux) Cross-stresses in the flow of air at reduced pressures, IUTAM Intern. Symposium, Second-order Effects in Elasticity, Plasticity and Fluid Dynamics, Haifa, 1962 (ed. M. REINER and D. ABIR), Pergamon Press, Oxford, 1964. 1962: (in collaboration with Z. KARNI) The general measure of deforma- tion, IUTAM Symposium, Haifa, ibid. 1964: (in collaboration with A. Foux) Cross-stresses in the flow of rare- fied air, 3rd Intern. Congress in the Aeronautical Sciences, Stock- holm, 1962, Spartan Books, Washington, D.C. 1965: (in collaboration with A. Foux) Cross-stresses in the flow of dif- ferent gases, Topics in Applied Mechanics—Schwerin Memorial Volume (ed. D. ABIR, F. OLLENDORFF and M. REINER), Elsevier Co., Amsterdam. 1965: (in collaboration with D. ABIR and H. MANOR) The solid viscosity of mild steel, ibid. 1965: Anomalous viscosity, Research Frontiers in Fluid Dynamics (ed. SEEGER and TEMPLE), pp. 171-91, Interscience Publishers, New York. 1965 : Second order effects, ibid., pp. 193-211. 1965: Second order stresses in the flow of gases, Proc. Intern. Con- gress Rheology, Providence, 1963, pp. 267-79. Selected List of Publications by Markus Reiner xiii 1966: Finite simple torsion of a circular cylinder, Israel J. Technology 4, 187-92. 1966: Deformation, Encyclopedia of Polymer Science and Technology 4, 620-47, John Wiley & Sons, New York. 1967: (in collaboration with Z. KARNI) The complete tensor expressions of the Green and Almansi measures of deformation, ZAMP 18, 131-2.