Strength Analysis in Geomechanics Xhi?b|
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by V*}zwm s6
S. Elsoufiev OT i3T1&
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Springer, 2007 ;>N ~ ,Q
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Foundations of Engineering Mechanics Mk[`HEO
Series Editors: V.I. Babitsky, J. Wittenburg &u-Bu;G.e
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It is hardly possible to find a single rheological law for all the soils. However, {9
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they have mechanical properties (elasticity, plasticity, creep, damage, etc.) qgNK!(kWpr
that are met in some special sciences, and basic equations of these disciplines Ks(U]G"V
can be applied to earth structures. This way is taken in this book. It represents L:-lqag!
the results that can be used as a base for computations in many fields of the mI#; pO2
Geomechanics in its wide sense. Deformation and fracture of many objects 7g9 ^Jn
include a row of important effects that must be taken into account. Some of ?M ^t4nj
them can be considered in the rheological law that, however, must be simple [<QWTMjR
enough to solve the problems for real objects. *.g?y6d
On the base of experiments and some theoretical investigations the constitutive wjOAgOC
equations that take into account large strains, a non-linear unsteady +ctv]'P _
creep, an influence of a stress state type, an initial anisotropy and a damage "'Uk0>d=_I
are introduced. The test results show that they can be used first of all to U.OX*-Cd
finding ultimate state of structures – for a wide variety of monotonous loadings Wh5O{G@Ut
when equivalent strain does not diminish, and include some interrupted, U I C? S
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 uszSFe]E
plasticity theory generalized here. At limit values of the exponent of a hardening ^<0 NIu}
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together zi
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with the basic relations of continuum mechanics they are used to describe the S8m&Rj3O&
deformation of many objects. Any of its stage can be taken as maximum _#m qg]W '
allowable one but it is more convenient to predict a failure according to the vWs c{9
criterion of infinite strains rate at the beginning of unstable deformation. The B}+9 U
method reveals the influence of the form and dimensions of the structure on "|`9 {/]
its ultimate state that are not considered by classical approaches. g/p9"eBpq
Certainly it is hardly possible to solve any real problem without some /}_c7+//
assumptions of geometrical type. Here the tasks are distinguished as antiplane ecpUp39\
(longitudinal shear), plane and axisymmetric problems. This allows yuEOQ\!(u
to consider a fracture of many real structures. The results are represented vp-7>Wj
by relations that can be applied directly and a computer is used (if necessary) P1 stL,
on a final stage of calculations. The method can be realized not only in :
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Geomechanics but also in other branches of industry and science. The whole E^a `IA
approach takes into account five types of non-linearity (three physical and Ba|}C(Ws?
two geometrical) and contains some new ideas, for example, the consideration L]N2r MM
of the fracture as a process, the difference between the body and the element H^;S}<pxW
of a material which only deforms and fails because it is in a structure, the PRC)GP&q
simplicity of some non-linear computations against linear ones (ideal plasticity NqE7 [wH
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the K/v-P <g
independence of maximum critical strain for brittle materials on the types of t<,p-TM]
structure and stress state, an advantage of deformation theories before flow 2Q|*xd4B^
ones and others. 3, I >.3
All this does not deny the classical methods that are also used in the book `yX+NRi(s
which is addressed to students, scientists and engineers who are busy with +W N>9V0H
strength problems.
