Strength Analysis in Geomechanics }K\ m.+%=d
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by d5 12Y[ R
S. Elsoufiev 2u'h,on?
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Springer, 2007 o9uir"=
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Foundations of Engineering Mechanics B" :u5_B
Series Editors: V.I. Babitsky, J. Wittenburg Se
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It is hardly possible to find a single rheological law for all the soils. However, Og~3eL[1%C
they have mechanical properties (elasticity, plasticity, creep, damage, etc.) \ )n' Ywr
that are met in some special sciences, and basic equations of these disciplines 6H}8^'/u
can be applied to earth structures. This way is taken in this book. It represents $N)b6(}F10
the results that can be used as a base for computations in many fields of the }Ii5[nRN
Geomechanics in its wide sense. Deformation and fracture of many objects |#=4]]>m
include a row of important effects that must be taken into account. Some of u|]`gsFZ\
them can be considered in the rheological law that, however, must be simple j -j,0!T~b
enough to solve the problems for real objects. MUd
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On the base of experiments and some theoretical investigations the constitutive wsLfp82
equations that take into account large strains, a non-linear unsteady DQOEntw
creep, an influence of a stress state type, an initial anisotropy and a damage x4vow F
are introduced. The test results show that they can be used first of all to g T~Yn~~b
finding ultimate state of structures – for a wide variety of monotonous loadings /xcl0oe(
when equivalent strain does not diminish, and include some interrupted, CERT`W%o
step-wise and even cycling changes of stresses. When the influence of time BTu_$ 5F
is negligible the basic expressions become the constitutive equations of the y6S:[Z{~A
plasticity theory generalized here. At limit values of the exponent of a hardening oaJnLd90W
law the last ones give the Hooke’s and the Prandtl’s diagrams. Together Zl+Ba
with the basic relations of continuum mechanics they are used to describe the Fz4g:8qdA
deformation of many objects. Any of its stage can be taken as maximum VDP \E<3"
allowable one but it is more convenient to predict a failure according to the Pe_FW8e#J
criterion of infinite strains rate at the beginning of unstable deformation. The rVo?I
method reveals the influence of the form and dimensions of the structure on U}Aoz|
its ultimate state that are not considered by classical approaches. 78 W&
Certainly it is hardly possible to solve any real problem without some oCftI':@
assumptions of geometrical type. Here the tasks are distinguished as antiplane >AT T<U=
(longitudinal shear), plane and axisymmetric problems. This allows ) 2jBhT
to consider a fracture of many real structures. The results are represented e2PM^1{_
by relations that can be applied directly and a computer is used (if necessary) lP:ll])p2
on a final stage of calculations. The method can be realized not only in 0'9z XJ"
Geomechanics but also in other branches of industry and science. The whole 1]<w ZV}.
approach takes into account five types of non-linearity (three physical and 9(;I+.;8k
two geometrical) and contains some new ideas, for example, the consideration ~'9>jpnw
of the fracture as a process, the difference between the body and the element n@Ar%%\
of a material which only deforms and fails because it is in a structure, the b: w {7
simplicity of some non-linear computations against linear ones (ideal plasticity V]$Tb xg
versus the Hooke’s law, unsteady creep instead of a steady one, etc.), the g/ict 2!
independence of maximum critical strain for brittle materials on the types of .s !qf!{V`
structure and stress state, an advantage of deformation theories before flow V
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ones and others. ?A4t
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All this does not deny the classical methods that are also used in the book <)
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which is addressed to students, scientists and engineers who are busy with aA -gl9
strength problems.
