Strength Analysis in Geomechanics @S>;t)\J
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by V\l@_%D[(v
S. Elsoufiev - leYR`P
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Springer, 2007 /{W6]6^
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Foundations of Engineering Mechanics k_Y7<z0G
Series Editors: V.I. Babitsky, J. Wittenburg !_B*Po
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It is hardly possible to find a single rheological law for all the soils. However, k]`-Y E
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) KeXt"U
that are met in some special sciences, and basic equations of these disciplines tCar:p4$
can be applied to earth structures. This way is taken in this book. It represents vbZ!NO!H
the results that can be used as a base for computations in many fields of the Xkg
Geomechanics in its wide sense. Deformation and fracture of many objects !ab ef.%:
include a row of important effects that must be taken into account. Some of ou<,c?nNM
them can be considered in the rheological law that, however, must be simple a;M{-G
enough to solve the problems for real objects. <^_crJONom
On the base of experiments and some theoretical investigations the constitutive ik;F@kdm`
equations that take into account large strains, a non-linear unsteady N]6t)Zv
creep, an influence of a stress state type, an initial anisotropy and a damage %~PT7"4
are introduced. The test results show that they can be used first of all to \j3dB
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finding ultimate state of structures – for a wide variety of monotonous loadings ju.pQ=PSX
when equivalent strain does not diminish, and include some interrupted, w*;"@2y;eY
step-wise and even cycling changes of stresses. When the influence of time lBAu@M
is negligible the basic expressions become the constitutive equations of the e?*Teb?R
plasticity theory generalized here. At limit values of the exponent of a hardening Y:, rN
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together V*@Y9G
with the basic relations of continuum mechanics they are used to describe the '3WtpsKA
deformation of many objects. Any of its stage can be taken as maximum
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allowable one but it is more convenient to predict a failure according to the c %Cbq0+2
criterion of infinite strains rate at the beginning of unstable deformation. The *f`P7q*
method reveals the influence of the form and dimensions of the structure on 5,g +OY=\
its ultimate state that are not considered by classical approaches. FF!PmfF'
Certainly it is hardly possible to solve any real problem without some 1?1Bz?EKF*
assumptions of geometrical type. Here the tasks are distinguished as antiplane 0y?;o*&U\
(longitudinal shear), plane and axisymmetric problems. This allows gZ7R^]
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to consider a fracture of many real structures. The results are represented K7K/P{@9[9
by relations that can be applied directly and a computer is used (if necessary) '[%#70*
on a final stage of calculations. The method can be realized not only in 't0M+_J
Geomechanics but also in other branches of industry and science. The whole L/`1K_\l
approach takes into account five types of non-linearity (three physical and :zLf~W
two geometrical) and contains some new ideas, for example, the consideration 9OW8/H&!
of the fracture as a process, the difference between the body and the element a !%,2|U
of a material which only deforms and fails because it is in a structure, the >eQ.y-
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simplicity of some non-linear computations against linear ones (ideal plasticity 4OpzGZ4+
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the MGt>:&s(]
independence of maximum critical strain for brittle materials on the types of $T^q>v2u
structure and stress state, an advantage of deformation theories before flow Qz#By V:
ones and others. b \ln XN
All this does not deny the classical methods that are also used in the book =CZRX'
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which is addressed to students, scientists and engineers who are busy with wCruj`$
strength problems.