|
Showing 1 - 4 of
4 matches in All Departments
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 . . . .
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."
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R383
R318
Discovery Miles 3 180
Loot
Nadine Gordimer
Paperback
(2)
R383
R318
Discovery Miles 3 180
Loot
Nadine Gordimer
Paperback
(2)
R383
R318
Discovery Miles 3 180
Hampstead
Diane Keaton, Brendan Gleeson, …
DVD
R63
Discovery Miles 630
|