Strength Analysis in Geomechanics ]rv\sD`[
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by gC1LQ!:;Oi
S. Elsoufiev "9caoPI0~
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Springer, 2007 `DYhGk
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Foundations of Engineering Mechanics 'zYS:W
Series Editors: V.I. Babitsky, J. Wittenburg Y9^l|,bm5
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It is hardly possible to find a single rheological law for all the soils. However, 23?u_?+4i
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) cfIC(d
that are met in some special sciences, and basic equations of these disciplines 9S%5Z>
can be applied to earth structures. This way is taken in this book. It represents ve
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the results that can be used as a base for computations in many fields of the UePkSz9EU
Geomechanics in its wide sense. Deformation and fracture of many objects 5Y *4a%"
include a row of important effects that must be taken into account. Some of oP,*H6)i
them can be considered in the rheological law that, however, must be simple R/~!km
enough to solve the problems for real objects. d0>U-.
On the base of experiments and some theoretical investigations the constitutive \ptO4E
equations that take into account large strains, a non-linear unsteady LSC[S:
creep, an influence of a stress state type, an initial anisotropy and a damage F!X0Wo=
are introduced. The test results show that they can be used first of all to ( cs
finding ultimate state of structures – for a wide variety of monotonous loadings 30sJ"hF9
when equivalent strain does not diminish, and include some interrupted, !8G)`'
step-wise and even cycling changes of stresses. When the influence of time jSp&\Wj b
is negligible the basic expressions become the constitutive equations of the ,8 4|qI
plasticity theory generalized here. At limit values of the exponent of a hardening nqy*>X`
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together H^-Y]{7
with the basic relations of continuum mechanics they are used to describe the Eg)24C R 4
deformation of many objects. Any of its stage can be taken as maximum B/4M;G~
allowable one but it is more convenient to predict a failure according to the ia5%
criterion of infinite strains rate at the beginning of unstable deformation. The :Qge1/
method reveals the influence of the form and dimensions of the structure on !,`'VQw$
its ultimate state that are not considered by classical approaches. cpOt?XYR~
Certainly it is hardly possible to solve any real problem without some > Z+*tq
assumptions of geometrical type. Here the tasks are distinguished as antiplane
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(longitudinal shear), plane and axisymmetric problems. This allows 6\7c:
to consider a fracture of many real structures. The results are represented x {NBhq(4
by relations that can be applied directly and a computer is used (if necessary) Lp&nO
on a final stage of calculations. The method can be realized not only in {?`rGJ{f
Geomechanics but also in other branches of industry and science. The whole 5k0iVpjQ
approach takes into account five types of non-linearity (three physical and in1rDN%Vi
two geometrical) and contains some new ideas, for example, the consideration '7'/+G'~&
of the fracture as a process, the difference between the body and the element 21v--wZ
of a material which only deforms and fails because it is in a structure, the :TTq
simplicity of some non-linear computations against linear ones (ideal plasticity b=EI?XwJ
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the N?qETp -:
independence of maximum critical strain for brittle materials on the types of (9u`(|x
structure and stress state, an advantage of deformation theories before flow J@-'IJ
ones and others. x Q"uC!Gu4
All this does not deny the classical methods that are also used in the book F7<mm7BGZ
which is addressed to students, scientists and engineers who are busy with 4V:W 8k 9D
strength problems.