Four Linear Continuum Theories - Continuum Mechanics of Anisotropic Materials - page 170

with a spring and a dashpot. These two branches are connected by two
transverse elements that are indicated by vertical lines. The rules for

formulating the overall force-deformation ( F ) relation for these spring

and dashpot models are: (1) the transverse elements that connect the two
branches remain parallel as the system is deformed; (2) the springs follow the
rule that F

d

/d t ). Let F L
and F U denote the forces in the upper and lower branches, respectively,

¼ k d , and the dashpots follow the rule that F ¼ d

(d

d D the

deflection of the dashpot and d S the deflection of the spring in series with

the dashpot. Construct the overall force-deformation ( F d ) relation for this

spring and dashpot model. List each step of your argument and explain
its rationale.

6.6 Relevant Literature

This chapter presents brief descriptions of four theories of material behavior.
There are many volumes written on each of these theories and there are entire
periodicals devoted to publishing recent results in each of these theories.
The purpose of this section is to mention some of the general literature associated
with each of these four theories, particularly that was drawn upon in the writing of
this chapter.
In heat conduction there are the texts of Carslaw and Jaeger (1959), Ozisik
(1980) and Jiji (2000). The thermoelasticity topic of Boley and Weiner (1960) also
contains much related material. The journals include the ASME Journal of Heat
Transfer and the International Journal of Heat and Mass Transfer .
Flow through porous media is addressed in topics by Bear ( 1972 ), Carman
( 1956 ), Scheidegger ( 1960 ) and others. Several of the topics on poroelasticity
mentioned in Chap. 8 contain much related material. The related journals
include Transport in Porous Media, Water Resources Research , and the Journal
of Hydrology .
The theory of elastic solids is described in the classical text of Love ( 1927 ), in
Timoshenko and Goodier ( 1951 ), Sokolnikoff ( 1956 ), Saada ( 1974 )andin
Gurtin ( 1972 ). Anisotropic elasticity is the subject of topics by Hearmon
( 1961 ), Lekhnitskii ( 1963 ), and Fedorov ( 1968 ). Current publications on
elasticity theory may be found in the Journal of Elasticity andinmanyrelated
journals such as the International Journal of Solids and Structures ,the Journal
of the Mechanics and Physics of Solids ,andtheASME Journal of Applied
Mechanics .
The theories associated with fluid behavior are described in the classical topics
of Lamb ( 1932 ), Prandtl and Tietjens ( 1934a , b ), and Schlichting ( 1960 ); Langois
( 1964 ) is an introduction to slow viscous flow. The current widely used text
is Batchleor ( 2000 ). There are many journals specializing in fluid mechanics;
the most broad and most successful is the Journal of Fluid Mechanics .