Strength Analysis in Geomechanics l2P=R)@{
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by 1HZO9cXJ
S. Elsoufiev ';=O 0)u
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Springer, 2007 xm~ `7~nFR
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Foundations of Engineering Mechanics bsli0FJSh'
Series Editors: V.I. Babitsky, J. Wittenburg +@f26O7$*
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It is hardly possible to find a single rheological law for all the soils. However, gZXi]m&
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) L`TLgH&?R
that are met in some special sciences, and basic equations of these disciplines 1R%.p7@5QU
can be applied to earth structures. This way is taken in this book. It represents ec;o\erPG
the results that can be used as a base for computations in many fields of the }R2u@%n{
Geomechanics in its wide sense. Deformation and fracture of many objects q YQl,w
include a row of important effects that must be taken into account. Some of f'RX6$}\1X
them can be considered in the rheological law that, however, must be simple eM6<%?b
enough to solve the problems for real objects. Dml;#'IF3
On the base of experiments and some theoretical investigations the constitutive u
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equations that take into account large strains, a non-linear unsteady [|$h*YK
creep, an influence of a stress state type, an initial anisotropy and a damage ;JT-kw6l5K
are introduced. The test results show that they can be used first of all to Q3~H{)[Kq
finding ultimate state of structures – for a wide variety of monotonous loadings khxnlry
when equivalent strain does not diminish, and include some interrupted, 2l'6.
step-wise and even cycling changes of stresses. When the influence of time
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is negligible the basic expressions become the constitutive equations of the nR~@#P\
plasticity theory generalized here. At limit values of the exponent of a hardening V f&zL
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law the last ones give the Hooke’s and the Prandtl’s diagrams. Together "HIRT E;&
with the basic relations of continuum mechanics they are used to describe the ^{`exCwM x
deformation of many objects. Any of its stage can be taken as maximum .~;\eW [
allowable one but it is more convenient to predict a failure according to the ?l{nk5,?-Y
criterion of infinite strains rate at the beginning of unstable deformation. The rs[T=C Q
method reveals the influence of the form and dimensions of the structure on 0#hlsfc] \
its ultimate state that are not considered by classical approaches. !f [_+CD
Certainly it is hardly possible to solve any real problem without some TIDO@ NwF
assumptions of geometrical type. Here the tasks are distinguished as antiplane Wn2NMXK
(longitudinal shear), plane and axisymmetric problems. This allows }($5k]]clP
to consider a fracture of many real structures. The results are represented tDcT%D {:
by relations that can be applied directly and a computer is used (if necessary) _TZRVa_
on a final stage of calculations. The method can be realized not only in /,yd+wcW#
Geomechanics but also in other branches of industry and science. The whole h[Y1?ln&h
approach takes into account five types of non-linearity (three physical and T!#GW/?
two geometrical) and contains some new ideas, for example, the consideration CAhXQ7w'Z
of the fracture as a process, the difference between the body and the element [9L:),&u
of a material which only deforms and fails because it is in a structure, the Zu [su>\
simplicity of some non-linear computations against linear ones (ideal plasticity 6nvz8f3*r]
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the C,r;VyW6BI
independence of maximum critical strain for brittle materials on the types of *i%d,w0+
structure and stress state, an advantage of deformation theories before flow ~36!?&eA8
ones and others. g3y ~bf
All this does not deny the classical methods that are also used in the book CH X #^0m.
which is addressed to students, scientists and engineers who are busy with W ac&b
strength problems.
