Strength Analysis in Geomechanics 6#CswSpS
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by a"U3h[;$y
S. Elsoufiev |w*s:p
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Springer, 2007 +)q ,4+K%}
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Foundations of Engineering Mechanics WcKDerc
Series Editors: V.I. Babitsky, J. Wittenburg QH(&Cu ,
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It is hardly possible to find a single rheological law for all the soils. However, MW rhVn{R
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) ]i`Q+q[
that are met in some special sciences, and basic equations of these disciplines zu
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can be applied to earth structures. This way is taken in this book. It represents d> ) =|
the results that can be used as a base for computations in many fields of the `Pj7:[."[
Geomechanics in its wide sense. Deformation and fracture of many objects SQf[1}$ .
include a row of important effects that must be taken into account. Some of V>)/z|[
them can be considered in the rheological law that, however, must be simple dR\yRC]I
enough to solve the problems for real objects. G2I%^.s
On the base of experiments and some theoretical investigations the constitutive :3Q:pKg
equations that take into account large strains, a non-linear unsteady R)Mkt8v
creep, an influence of a stress state type, an initial anisotropy and a damage 1K@ieVc
are introduced. The test results show that they can be used first of all to A ~vx,|I
finding ultimate state of structures – for a wide variety of monotonous loadings o}KVT% }
when equivalent strain does not diminish, and include some interrupted, t.;._'
step-wise and even cycling changes of stresses. When the influence of time #!O)-dyF
is negligible the basic expressions become the constitutive equations of the oz=ULPZ%
plasticity theory generalized here. At limit values of the exponent of a hardening 06AgY0\
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together d"-I^|[OM
with the basic relations of continuum mechanics they are used to describe the \a;xJzc9
deformation of many objects. Any of its stage can be taken as maximum hizM}d-"C
allowable one but it is more convenient to predict a failure according to the hIqU idJod
criterion of infinite strains rate at the beginning of unstable deformation. The u,8)M' UU
method reveals the influence of the form and dimensions of the structure on ZJ2
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its ultimate state that are not considered by classical approaches. tP! %(+V
Certainly it is hardly possible to solve any real problem without some v4|TQ8!wR
assumptions of geometrical type. Here the tasks are distinguished as antiplane M}11 tUl
(longitudinal shear), plane and axisymmetric problems. This allows _w?!Mu
to consider a fracture of many real structures. The results are represented [#@lsI
by relations that can be applied directly and a computer is used (if necessary) ^ fC2o%3^
on a final stage of calculations. The method can be realized not only in vJ&D>Vh4e
Geomechanics but also in other branches of industry and science. The whole z-gMk@l
approach takes into account five types of non-linearity (three physical and zC)JOykI%
two geometrical) and contains some new ideas, for example, the consideration 2=K|kp5
of the fracture as a process, the difference between the body and the element D
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of a material which only deforms and fails because it is in a structure, the 6ZHeAb]"
simplicity of some non-linear computations against linear ones (ideal plasticity L)U*dY
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the P/ 6$TgQ
independence of maximum critical strain for brittle materials on the types of C=&n1 /
structure and stress state, an advantage of deformation theories before flow Rjq\$ aY}%
ones and others. g4,ldr"D
All this does not deny the classical methods that are also used in the book $ dI
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which is addressed to students, scientists and engineers who are busy with 084Us
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strength problems.
