Limiting Equilibrium of a Material With Load Dependent Strength Properties

  • Oxana Sadovskaya
  • Vladimir Sadovskii
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 21)


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.


Variational Inequality Granular Material Displacement Field Limit Load Localization Line 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.ICM SB RASKrasnoyarskRussia

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