Strength Analysis in Geomechanics |AuN5|ob I
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by b 9F=}.4
S. Elsoufiev q A#!3<
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Springer, 2007 6}n>Nb;L"
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Foundations of Engineering Mechanics tlQ3 BKp
Series Editors: V.I. Babitsky, J. Wittenburg 9eH(FB
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It is hardly possible to find a single rheological law for all the soils. However, b,$H!V *
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) W$v5o9\Px
that are met in some special sciences, and basic equations of these disciplines
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can be applied to earth structures. This way is taken in this book. It represents `\(Fax
the results that can be used as a base for computations in many fields of the g(>;Z@Y
Geomechanics in its wide sense. Deformation and fracture of many objects 8BhLO.( <O
include a row of important effects that must be taken into account. Some of 8 POrD8B
them can be considered in the rheological law that, however, must be simple aYkm]w;C
enough to solve the problems for real objects. %f#3;tpC8
On the base of experiments and some theoretical investigations the constitutive Q: [d
equations that take into account large strains, a non-linear unsteady S e%FqI
creep, an influence of a stress state type, an initial anisotropy and a damage Nf%jLK~
are introduced. The test results show that they can be used first of all to ="P 3TP
finding ultimate state of structures – for a wide variety of monotonous loadings lnEc5J@c>i
when equivalent strain does not diminish, and include some interrupted, pe Y( 4#
step-wise and even cycling changes of stresses. When the influence of time ~ 6 1O
is negligible the basic expressions become the constitutive equations of the 6cb;iA
plasticity theory generalized here. At limit values of the exponent of a hardening DAj@wn3K?
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together , pq<.?&E
with the basic relations of continuum mechanics they are used to describe the Y]0oF_ :7
deformation of many objects. Any of its stage can be taken as maximum !r,ZyJU
allowable one but it is more convenient to predict a failure according to the iKu[j)F
criterion of infinite strains rate at the beginning of unstable deformation. The PnJr
method reveals the influence of the form and dimensions of the structure on sT?Qlj 'Zd
its ultimate state that are not considered by classical approaches. =4/LixsV|
Certainly it is hardly possible to solve any real problem without some KIps {_J[<
assumptions of geometrical type. Here the tasks are distinguished as antiplane t^)q[g
(longitudinal shear), plane and axisymmetric problems. This allows #9,!IW]l
to consider a fracture of many real structures. The results are represented {l-,Jbfi`
by relations that can be applied directly and a computer is used (if necessary) {
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on a final stage of calculations. The method can be realized not only in eO t T*
Geomechanics but also in other branches of industry and science. The whole 5][ Rvu0
approach takes into account five types of non-linearity (three physical and HIcx "y
two geometrical) and contains some new ideas, for example, the consideration DQDt*Uj,
of the fracture as a process, the difference between the body and the element U\&kT/6vh
of a material which only deforms and fails because it is in a structure, the U59uP
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simplicity of some non-linear computations against linear ones (ideal plasticity :@I?JSi
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the ?"$W=*P\o
independence of maximum critical strain for brittle materials on the types of /t ikLJ
structure and stress state, an advantage of deformation theories before flow y/K% F,WMf
ones and others. GrGgR7eC#P
All this does not deny the classical methods that are also used in the book JUok@6
which is addressed to students, scientists and engineers who are busy with 5r.\maW
strength problems.
