Strength Analysis in Geomechanics vxfh1B&
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by CX2q7azG
S. Elsoufiev a[9OtZX<
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Springer, 2007 ml
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Foundations of Engineering Mechanics E
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Series Editors: V.I. Babitsky, J. Wittenburg n ylIP */
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It is hardly possible to find a single rheological law for all the soils. However, {Q3#]Vu
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) 5m;wMW <
that are met in some special sciences, and basic equations of these disciplines zEL[%(fnc
can be applied to earth structures. This way is taken in this book. It represents u>Kvub
the results that can be used as a base for computations in many fields of the "k@/Z7=
Geomechanics in its wide sense. Deformation and fracture of many objects ' F<e)D?
include a row of important effects that must be taken into account. Some of u, k8i:JY
them can be considered in the rheological law that, however, must be simple m!>'}z
enough to solve the problems for real objects. bWzc=03
On the base of experiments and some theoretical investigations the constitutive yxq!. 72
equations that take into account large strains, a non-linear unsteady X-^Oz@.>
creep, an influence of a stress state type, an initial anisotropy and a damage ZQ8 Aak
are introduced. The test results show that they can be used first of all to
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finding ultimate state of structures – for a wide variety of monotonous loadings .VV!$;
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when equivalent strain does not diminish, and include some interrupted, -5B([jHgR
step-wise and even cycling changes of stresses. When the influence of time F4l6PGxF&\
is negligible the basic expressions become the constitutive equations of the ~ a|Q[tiV]
plasticity theory generalized here. At limit values of the exponent of a hardening !a&F:Fbm
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together ?UZ yu 4O%
with the basic relations of continuum mechanics they are used to describe the GM92yi!8
deformation of many objects. Any of its stage can be taken as maximum D#AxgF_He
allowable one but it is more convenient to predict a failure according to the +:8YMM#9V
criterion of infinite strains rate at the beginning of unstable deformation. The O&RHCR- \
method reveals the influence of the form and dimensions of the structure on ;a77YL TQ
its ultimate state that are not considered by classical approaches. eWs^[^c.<
Certainly it is hardly possible to solve any real problem without some Z
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assumptions of geometrical type. Here the tasks are distinguished as antiplane mT$tAwzTC{
(longitudinal shear), plane and axisymmetric problems. This allows "N"k8,LH
to consider a fracture of many real structures. The results are represented im\Ws./
by relations that can be applied directly and a computer is used (if necessary) jpS#'h
on a final stage of calculations. The method can be realized not only in yU lQPrNX
Geomechanics but also in other branches of industry and science. The whole =!Cvu.~},
approach takes into account five types of non-linearity (three physical and Bd[}A9O[
two geometrical) and contains some new ideas, for example, the consideration C#cEMKa
of the fracture as a process, the difference between the body and the element tHo/uW_~I
of a material which only deforms and fails because it is in a structure, the aM1JG$+7G
simplicity of some non-linear computations against linear ones (ideal plasticity LKG|S<s
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the `-\JjMSQ1
independence of maximum critical strain for brittle materials on the types of !ry+ r!"
structure and stress state, an advantage of deformation theories before flow AV`7> @
ones and others. a"N_zGf2$
All this does not deny the classical methods that are also used in the book 9~ af\G
which is addressed to students, scientists and engineers who are busy with Ct3 3S+y
strength problems.
