W. Noll – författare

German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc­ torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.

German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc­ torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.

The term "dislocation" is used in several different senses in the literature of mechanics. In the elassic work of VOLTERRA, WEINGARTEN, and SOMIGLIANA, it refers to particular solutions of the equations of linear elasticity, in which a con­ tinuous field of strain does not correspond, globally, to a continuous field of dis­ placement. The configuration of the body so obtained, even when that body is free of all load, is subject to interior stress that does not vanish, and in general no deformation of the body as a wh oIe can bring it into a stress-free configuration. Nevertheless, if any sufficiently sm all part of the body is considered by itself, a configuration for it in which the stress is everywhere zero may be found at once. In this work constitutiL"e assumptions provide the basic data. These consist in prescribed stress-free configurations for each material point and in prescribed elastic moduli governing the response to deformation from the stress-free configuration at each material point. Everything follows from these data, ineluding the dislocations present, if any. In particular, the common boundary-value problems of linear elasticity may be set and solved for the dislocated body.

The term "dislocation" is used in several different senses in the literature of mechanics. In the elassic work of VOLTERRA, WEINGARTEN, and SOMIGLIANA, it refers to particular solutions of the equations of linear elasticity, in which a con­ tinuous field of strain does not correspond, globally, to a continuous field of dis­ placement. The configuration of the body so obtained, even when that body is free of all load, is subject to interior stress that does not vanish, and in general no deformation of the body as a wh oIe can bring it into a stress-free configuration. Nevertheless, if any sufficiently sm all part of the body is considered by itself, a configuration for it in which the stress is everywhere zero may be found at once. In this work constitutiL"e assumptions provide the basic data. These consist in prescribed stress-free configurations for each material point and in prescribed elastic moduli governing the response to deformation from the stress-free configuration at each material point. Everything follows from these data, ineluding the dislocations present, if any. In particular, the common boundary-value problems of linear elasticity may be set and solved for the dislocated body.

We here attempt to give a complete but concise treatment of the theory of steady viscometric flows of simple (non-Newtonian) fluids and to use that theory to discuss the design and interpretation of ex­ periments. We are able to present the theory with less mathematical machinery than was used in our original papers, partly because this Tract has more limited aims than those papers, and partly because we employ a method, found by Noll and published here for the first time, for dealing with visco metric flows without the apparatus of rela­ tive Cauchy-Green tensors and reduced constitutive equations. To make the theory accessible to students not familiar with modern mathematics, we have added to our Tract an appendix explaining some of the mathe­ matical concepts essential to continuum physics. Pittsburgh, July 1965 BERNARD D. COLEMAN HERSHEL MARKOVITZ WALTER NOLL CONTENTS I. Introduction page 1. Limitations of the Classical Theory of Navier and Stokes. 1 5 2. Incompressible Simple Fluids. . . . . . . . . . . . 3. Plan and Scope of this Monograph . . . . . . . . . 7 II. Theory of Incompressible Simple Fluids 4. Kinematics. . . . . . . . . . . . 10 5. The Dynamical Equations . . . . . . . . . . . 12 6. The Principle of Material Objectivity . . . . . . 14 7. The Definition of an Incompressible Simple Fluid . 17 8. Static Behavior of Simple Fluids . . . . . . . . 19 III. General Theory of Viscometric Flows 9. The Kinematics of Simple Shearing Flow 21 10. The Viscometric Functions . . . . . . . . . . 22 11. The Dynamics of Simple Shearing Flow; Viscosity 26 12. The Definition of a Viscometric Flow 29 13. Curvilineal Flows. . . . . . . . 30 1. Kinematical Description . . . .