Strength Analysis in Geomechanics B]]_rl,
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by ^.jIus5
S. Elsoufiev YhFB*D;
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Springer, 2007 bnLvJ]i)
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Foundations of Engineering Mechanics W|~Lmdzj
Series Editors: V.I. Babitsky, J. Wittenburg V_Kpb*3
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It is hardly possible to find a single rheological law for all the soils. However, Q)yhpwrX
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) t6_6Bl:
that are met in some special sciences, and basic equations of these disciplines 1g{`1[.QO
can be applied to earth structures. This way is taken in this book. It represents }K9 V r!
the results that can be used as a base for computations in many fields of the %*]3j^b Q+
Geomechanics in its wide sense. Deformation and fracture of many objects cX"[#Em#
include a row of important effects that must be taken into account. Some of "XMTj <D
them can be considered in the rheological law that, however, must be simple lY!`< _Am
enough to solve the problems for real objects. 7 }(LO^,A
On the base of experiments and some theoretical investigations the constitutive [>&Nhn0 iY
equations that take into account large strains, a non-linear unsteady ]hTYh^' e
creep, an influence of a stress state type, an initial anisotropy and a damage ^dH#n~Wx0
are introduced. The test results show that they can be used first of all to hu[=9#''$
finding ultimate state of structures – for a wide variety of monotonous loadings h";G vjy
when equivalent strain does not diminish, and include some interrupted, A- IpE
step-wise and even cycling changes of stresses. When the influence of time VztalwI
is negligible the basic expressions become the constitutive equations of the Rj9M E,u
plasticity theory generalized here. At limit values of the exponent of a hardening "?lirOD
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together i{PRjkR
with the basic relations of continuum mechanics they are used to describe the @5Q}o3.zA-
deformation of many objects. Any of its stage can be taken as maximum 2qKo|'gL`
allowable one but it is more convenient to predict a failure according to the K ) $.0S9d
criterion of infinite strains rate at the beginning of unstable deformation. The RvV4SlZz
method reveals the influence of the form and dimensions of the structure on x_{ua0BLDf
its ultimate state that are not considered by classical approaches. z.oDH<1
Certainly it is hardly possible to solve any real problem without some -QCo]:cp
assumptions of geometrical type. Here the tasks are distinguished as antiplane j,eeQ KH
(longitudinal shear), plane and axisymmetric problems. This allows "t~I;%$[
to consider a fracture of many real structures. The results are represented 9I=J#Hi|+
by relations that can be applied directly and a computer is used (if necessary) wlBdA
on a final stage of calculations. The method can be realized not only in ULMG"."IH
Geomechanics but also in other branches of industry and science. The whole ~}w(YQy=y
approach takes into account five types of non-linearity (three physical and )r uC_)
two geometrical) and contains some new ideas, for example, the consideration ]oP2T:A
of the fracture as a process, the difference between the body and the element [ivz/r(Rj
of a material which only deforms and fails because it is in a structure, the 6'395x_ .\
simplicity of some non-linear computations against linear ones (ideal plasticity yAR'' >
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the g1muT.W]S
independence of maximum critical strain for brittle materials on the types of u].=b$wHHM
structure and stress state, an advantage of deformation theories before flow En A) Rz
ones and others. +[`N|x<
All this does not deny the classical methods that are also used in the book |f'U_nE#R/
which is addressed to students, scientists and engineers who are busy with o+`W
strength problems.
