Strength Analysis in Geomechanics m,KG}KX
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by Coz\fL
S. Elsoufiev )
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Springer, 2007 7M*&^P\}es
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Foundations of Engineering Mechanics 5 s3!{zT{
Series Editors: V.I. Babitsky, J. Wittenburg 5[3vu p?
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It is hardly possible to find a single rheological law for all the soils. However, WPT0=Hqp7
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) R&Y+x;({
that are met in some special sciences, and basic equations of these disciplines . _j9^Ll
can be applied to earth structures. This way is taken in this book. It represents 7}>7@ W8
the results that can be used as a base for computations in many fields of the `R@1 Sc<*|
Geomechanics in its wide sense. Deformation and fracture of many objects %fB]N
include a row of important effects that must be taken into account. Some of Hd
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them can be considered in the rheological law that, however, must be simple 9?$Qk0jc
enough to solve the problems for real objects. Vx$ ?)&
On the base of experiments and some theoretical investigations the constitutive <7-:flQz~
equations that take into account large strains, a non-linear unsteady T. \=R
creep, an influence of a stress state type, an initial anisotropy and a damage ;oW#>!HrY
are introduced. The test results show that they can be used first of all to *@`Sx' 5!
finding ultimate state of structures – for a wide variety of monotonous loadings : p# 5nYi
when equivalent strain does not diminish, and include some interrupted, 'jAX&7G`
step-wise and even cycling changes of stresses. When the influence of time P%w)*);
is negligible the basic expressions become the constitutive equations of the yClX!OL
plasticity theory generalized here. At limit values of the exponent of a hardening -?L~\WJAL
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together A)"?GK{*
with the basic relations of continuum mechanics they are used to describe the KwO;ICdJ
deformation of many objects. Any of its stage can be taken as maximum PhTMXv<cE
allowable one but it is more convenient to predict a failure according to the J?VMQTa/+
criterion of infinite strains rate at the beginning of unstable deformation. The 5Fa.X|R~
method reveals the influence of the form and dimensions of the structure on *9J >3
its ultimate state that are not considered by classical approaches. o9I=zAGjy
Certainly it is hardly possible to solve any real problem without some ?:DeOBAb
assumptions of geometrical type. Here the tasks are distinguished as antiplane Gf``0F)
(longitudinal shear), plane and axisymmetric problems. This allows j4pxu/2
to consider a fracture of many real structures. The results are represented zf+jQ
by relations that can be applied directly and a computer is used (if necessary) LY Y3*d
on a final stage of calculations. The method can be realized not only in 9yla &XTD
Geomechanics but also in other branches of industry and science. The whole %
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approach takes into account five types of non-linearity (three physical and DJ)Q,l*|N9
two geometrical) and contains some new ideas, for example, the consideration MvV\?Lzj
of the fracture as a process, the difference between the body and the element >@?!-Fy5
of a material which only deforms and fails because it is in a structure, the h"R{{y f2
simplicity of some non-linear computations against linear ones (ideal plasticity }7)iLfi
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the E6+c{41B
independence of maximum critical strain for brittle materials on the types of gE r @L
structure and stress state, an advantage of deformation theories before flow &c[.&L,w4
ones and others. Eod'Esye5
All this does not deny the classical methods that are also used in the book *Ae>
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which is addressed to students, scientists and engineers who are busy with +9EG6"..@H
strength problems.
