Strength Analysis in Geomechanics yoW>
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by .C?GW1[c~@
S. Elsoufiev b[0S=e
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Springer, 2007 cz>mhD
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Foundations of Engineering Mechanics
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Series Editors: V.I. Babitsky, J. Wittenburg Um'Ro 4
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It is hardly possible to find a single rheological law for all the soils. However, ]|y}\7Aa
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) <S {7Ro
that are met in some special sciences, and basic equations of these disciplines Ge1duRGa
can be applied to earth structures. This way is taken in this book. It represents d q2@6xd
the results that can be used as a base for computations in many fields of the p }BG w:=
Geomechanics in its wide sense. Deformation and fracture of many objects Pl?}>G
include a row of important effects that must be taken into account. Some of Z+,CL/
them can be considered in the rheological law that, however, must be simple RxMoD.kx
enough to solve the problems for real objects. ,\}k~ U99
On the base of experiments and some theoretical investigations the constitutive !U[:5@s06
equations that take into account large strains, a non-linear unsteady r} ,lu=em
creep, an influence of a stress state type, an initial anisotropy and a damage |G=FqAX H
are introduced. The test results show that they can be used first of all to #@q1Ko!NZ
finding ultimate state of structures – for a wide variety of monotonous loadings ]7l{g9?ZtV
when equivalent strain does not diminish, and include some interrupted, [x|)}P7%s
step-wise and even cycling changes of stresses. When the influence of time sy=dY@W^
is negligible the basic expressions become the constitutive equations of the lfRH`u
plasticity theory generalized here. At limit values of the exponent of a hardening V:8@)Hc=
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together v!KJ|c@m
with the basic relations of continuum mechanics they are used to describe the _1\poAy
deformation of many objects. Any of its stage can be taken as maximum q55M8B 4w
allowable one but it is more convenient to predict a failure according to the LGXZx}4@;
criterion of infinite strains rate at the beginning of unstable deformation. The c`pYc
method reveals the influence of the form and dimensions of the structure on :-U53}Iy
its ultimate state that are not considered by classical approaches. :^5>wDu{
Certainly it is hardly possible to solve any real problem without some -zR. 'x%
assumptions of geometrical type. Here the tasks are distinguished as antiplane $-e=tWkg v
(longitudinal shear), plane and axisymmetric problems. This allows D>S8$]^Dm
to consider a fracture of many real structures. The results are represented ;8uHRc dQ
by relations that can be applied directly and a computer is used (if necessary) ~7dF/Nn5
on a final stage of calculations. The method can be realized not only in cX Ma \#P
Geomechanics but also in other branches of industry and science. The whole .}`V I`z*
approach takes into account five types of non-linearity (three physical and 8,H~4Ce3
two geometrical) and contains some new ideas, for example, the consideration y s/vI/e\
of the fracture as a process, the difference between the body and the element 0a@c/ XGBp
of a material which only deforms and fails because it is in a structure, the C&e8a9*,(a
simplicity of some non-linear computations against linear ones (ideal plasticity A^t"MYX@
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the >ks3W Mm
independence of maximum critical strain for brittle materials on the types of z41D^ }b
structure and stress state, an advantage of deformation theories before flow Pm~,Ky&Hl
ones and others. q{[1fE"[K4
All this does not deny the classical methods that are also used in the book ^SgN(-QH
which is addressed to students, scientists and engineers who are busy with 16 L"^EYq
strength problems.
