Strength Analysis in Geomechanics 0c.s
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by SYeadsvF
S. Elsoufiev FG3UZVUg9
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Springer, 2007 cw&Hgjj2
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Foundations of Engineering Mechanics <X TU8G
Series Editors: V.I. Babitsky, J. Wittenburg qjJBcu_C'S
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It is hardly possible to find a single rheological law for all the soils. However, %xlqF<
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) 2RF^s.W
that are met in some special sciences, and basic equations of these disciplines E@a3~a
can be applied to earth structures. This way is taken in this book. It represents
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the results that can be used as a base for computations in many fields of the w|mb4AyL{?
Geomechanics in its wide sense. Deformation and fracture of many objects 4RKW
include a row of important effects that must be taken into account. Some of iDl;!b&V.
them can be considered in the rheological law that, however, must be simple C^t(^9
enough to solve the problems for real objects. <)g8yA
On the base of experiments and some theoretical investigations the constitutive iFSJL,QZ3
equations that take into account large strains, a non-linear unsteady q;5i4|
creep, an influence of a stress state type, an initial anisotropy and a damage 9p$V)qdX
are introduced. The test results show that they can be used first of all to #{r#;+
finding ultimate state of structures – for a wide variety of monotonous loadings GN#<yv$av
when equivalent strain does not diminish, and include some interrupted, %2'A
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step-wise and even cycling changes of stresses. When the influence of time $(s\{(Wn
is negligible the basic expressions become the constitutive equations of the L_Q#(in
plasticity theory generalized here. At limit values of the exponent of a hardening gIR^)m
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together M:Er_,E
with the basic relations of continuum mechanics they are used to describe the UE _fpq
deformation of many objects. Any of its stage can be taken as maximum #8{F9w<Rf
allowable one but it is more convenient to predict a failure according to the X u"R^
criterion of infinite strains rate at the beginning of unstable deformation. The Q|}aR:4
method reveals the influence of the form and dimensions of the structure on ]DFXPV
its ultimate state that are not considered by classical approaches. _!xD8Di#
Certainly it is hardly possible to solve any real problem without some z
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assumptions of geometrical type. Here the tasks are distinguished as antiplane 0U66y6
(longitudinal shear), plane and axisymmetric problems. This allows sDqe(x}a
to consider a fracture of many real structures. The results are represented h9$ Fx
by relations that can be applied directly and a computer is used (if necessary) E{=2\Wkcp
on a final stage of calculations. The method can be realized not only in #5sD{:f`
Geomechanics but also in other branches of industry and science. The whole |VOg\[f
approach takes into account five types of non-linearity (three physical and *fO3]+)d+
two geometrical) and contains some new ideas, for example, the consideration BhpOXqg
of the fracture as a process, the difference between the body and the element ?!w^`D0}o
of a material which only deforms and fails because it is in a structure, the R8*Q$rH<
simplicity of some non-linear computations against linear ones (ideal plasticity m,3er*t{
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the 6
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independence of maximum critical strain for brittle materials on the types of M"q[ p
structure and stress state, an advantage of deformation theories before flow U]qav,^[
ones and others. ?&WYjTU]H
All this does not deny the classical methods that are also used in the book `Yc_5&"
which is addressed to students, scientists and engineers who are busy with "_L?2ta
strength problems.