Strength Analysis in Geomechanics n.y72-& v
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S. Elsoufiev * #;rp~
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Springer, 2007 bct&ge7YX
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Foundations of Engineering Mechanics 1p&?MxLN-a
Series Editors: V.I. Babitsky, J. Wittenburg /BVN JNhz
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It is hardly possible to find a single rheological law for all the soils. However, |P2 GL3NR
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) ASaG }h
that are met in some special sciences, and basic equations of these disciplines Z-H Kdv!d
can be applied to earth structures. This way is taken in this book. It represents W^&t8d2
the results that can be used as a base for computations in many fields of the mI in'M
Geomechanics in its wide sense. Deformation and fracture of many objects 'eqvK|Uj:
include a row of important effects that must be taken into account. Some of sa+ :c{
them can be considered in the rheological law that, however, must be simple xMhR;lKY
enough to solve the problems for real objects. K"b vUH
On the base of experiments and some theoretical investigations the constitutive uW[s?
equations that take into account large strains, a non-linear unsteady ^m8\fCA*
creep, an influence of a stress state type, an initial anisotropy and a damage bTHa;* `
are introduced. The test results show that they can be used first of all to OG 5n9sx
finding ultimate state of structures – for a wide variety of monotonous loadings foE2rV/Y
when equivalent strain does not diminish, and include some interrupted, 4 '9h^C&
step-wise and even cycling changes of stresses. When the influence of time 6aQ{EO-]'=
is negligible the basic expressions become the constitutive equations of the Ok({Al1A,w
plasticity theory generalized here. At limit values of the exponent of a hardening }.zg VL L
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together [dU/;Sk5
with the basic relations of continuum mechanics they are used to describe the 9LJ/m\bi
deformation of many objects. Any of its stage can be taken as maximum +I\ bs.84
allowable one but it is more convenient to predict a failure according to the o(~JZi k
criterion of infinite strains rate at the beginning of unstable deformation. The %v~j1 0e
method reveals the influence of the form and dimensions of the structure on o`j%$K4?5
its ultimate state that are not considered by classical approaches. oRWsi/Zf
Certainly it is hardly possible to solve any real problem without some TJsT .DWW~
assumptions of geometrical type. Here the tasks are distinguished as antiplane 6nGDoW#
(longitudinal shear), plane and axisymmetric problems. This allows F<-Pbtw
to consider a fracture of many real structures. The results are represented ;N"XW=F4e
by relations that can be applied directly and a computer is used (if necessary) !b _<_Y{l
on a final stage of calculations. The method can be realized not only in NK#Dq&W+&
Geomechanics but also in other branches of industry and science. The whole N}F G%a
approach takes into account five types of non-linearity (three physical and J;q3
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two geometrical) and contains some new ideas, for example, the consideration JG}U,{7(
of the fracture as a process, the difference between the body and the element o~>p=5t
of a material which only deforms and fails because it is in a structure, the EUna_ 4=
simplicity of some non-linear computations against linear ones (ideal plasticity vW)GUAF[
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the FT (EH
independence of maximum critical strain for brittle materials on the types of _ 9
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structure and stress state, an advantage of deformation theories before flow [sN n^x
ones and others. "hlIGJ?_=
All this does not deny the classical methods that are also used in the book <U,T*Ql1x
which is addressed to students, scientists and engineers who are busy with `8'T*KU
strength problems.
