Strength Analysis in Geomechanics ,ayEZ#4.m
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by 'Q= ;I
S. Elsoufiev - VJx)g
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Springer, 2007 UN'n~d @~
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Foundations of Engineering Mechanics +ydd"`
Series Editors: V.I. Babitsky, J. Wittenburg %tP*_d:
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It is hardly possible to find a single rheological law for all the soils. However, _tHhS@
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) igo9~.
that are met in some special sciences, and basic equations of these disciplines 8xENzTR
can be applied to earth structures. This way is taken in this book. It represents [2-n*a(q
the results that can be used as a base for computations in many fields of the ) (YNNu
Geomechanics in its wide sense. Deformation and fracture of many objects X&WP.n)
include a row of important effects that must be taken into account. Some of a Vu!Qk=Z/
them can be considered in the rheological law that, however, must be simple u@dvF zc
enough to solve the problems for real objects. 0Fb ];:a
On the base of experiments and some theoretical investigations the constitutive eyK xnBz
equations that take into account large strains, a non-linear unsteady l_}d Q&R
creep, an influence of a stress state type, an initial anisotropy and a damage *b>RUESF
are introduced. The test results show that they can be used first of all to Jw _>I
finding ultimate state of structures – for a wide variety of monotonous loadings di/Q Jrw
when equivalent strain does not diminish, and include some interrupted, R ` ViRJh
step-wise and even cycling changes of stresses. When the influence of time ! 64Tx
is negligible the basic expressions become the constitutive equations of the O &<p
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plasticity theory generalized here. At limit values of the exponent of a hardening "r4 6Rfa
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together (T*$4KGV
with the basic relations of continuum mechanics they are used to describe the 42]7N3:'
deformation of many objects. Any of its stage can be taken as maximum `rVru= zoy
allowable one but it is more convenient to predict a failure according to the 4 -.W~C'Q
criterion of infinite strains rate at the beginning of unstable deformation. The o6vn l
method reveals the influence of the form and dimensions of the structure on Dy.i^`7\
its ultimate state that are not considered by classical approaches. K.xABKPVc
Certainly it is hardly possible to solve any real problem without some 9nN1f@Y
assumptions of geometrical type. Here the tasks are distinguished as antiplane d%|l)JF*5
(longitudinal shear), plane and axisymmetric problems. This allows Wu
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to consider a fracture of many real structures. The results are represented X8ulaa
by relations that can be applied directly and a computer is used (if necessary) FGi7 KV=N
on a final stage of calculations. The method can be realized not only in #DgHF*GG+>
Geomechanics but also in other branches of industry and science. The whole nsI+04[F
approach takes into account five types of non-linearity (three physical and {R ),7 U8
two geometrical) and contains some new ideas, for example, the consideration 0Ncpi=6
of the fracture as a process, the difference between the body and the element $6 Q^u r:
of a material which only deforms and fails because it is in a structure, the <-k !
simplicity of some non-linear computations against linear ones (ideal plasticity l(NQk> w
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the 3aq'JVq
independence of maximum critical strain for brittle materials on the types of dJgLS^1E
structure and stress state, an advantage of deformation theories before flow ai-s9r'MI?
ones and others. [eD0L7 1[
All this does not deny the classical methods that are also used in the book =|-= 4.b+|
which is addressed to students, scientists and engineers who are busy with $Wj= V
strength problems.
