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2012 | OriginalPaper | Chapter

5. Limiting Equilibrium of a Material With Load Dependent Strength Properties

Authors : Oxana Sadovskaya, Vladimir Sadovskii

Published in: Mathematical Modeling in Mechanics of Granular Materials

Publisher: Springer Berlin Heidelberg

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Abstract

Solvability of static boundary-value problems within the framework of a model describing small strains in a material with load dependent strength properties, for example at tension and compression, is studied. A generalization of the static and kinematic theorems of the theory of limiting equilibrium is given. As an example of the application of the kinematic theorem, an upper estimate of the limit load and of the angle of departure of linear zone of the strain localization for the problem on discontinuity of a notched sample under the action of pressure on the edges of a notch is found. It is shown that logarithmic spirals serve as localization lines. With the help of two-sided estimates, an expression for the angle of natural slope of an ideal granular material is obtained. For the numerical solution of boundary-value problems, an iterative algorithm based on the finite-element approximation of a model is worked out. Results of computations which confirm the obtained estimating solutions are presented.

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previous chapter Spatial Constitutive Relationships
next chapter Elastic–Plastic Waves in a Loosened Material
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Metadata
Title
Limiting Equilibrium of a Material With Load Dependent Strength Properties
Authors
Oxana Sadovskaya
Vladimir Sadovskii
Copyright Year
2012
Publisher
Springer Berlin Heidelberg
Book
Mathematical Modeling in Mechanics of Granular Materials

Print ISBN: 978-3-642-29052-7

Electronic ISBN: 978-3-642-29053-4

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-3-642-29053-4_5

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