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Equivalent stress concept for limit state analysis

: Kolupaev, Vladimir, A.


Cham: Springer International Publishing, 2018, VIII, 292 S.
Advanced structured materials, 86
ISBN: 978-3-319-73048-6 (Print)
ISBN: 978-3-319-73049-3 (Online)
ISBN: 3-319-73048-7
Fraunhofer LBF ()

In this book, criteria for isotropic materials based on the equivalent stress concept are discussed. These criteria are widely applied in the limit state analysis. For general use, they are formulated in the invariants of the stress tensor. At first, so-called classical hypotheses which are useful in the case of absolutely brittle or ideal ductile material behavior are presented. Different techniques of model visualization are discussed for clear evaluation. Nine tests for basic stress states are suggested and imaged in different planes together with the criteria. At second, standard criteria describing the intermediate range between the absolutely brittle and ideal ductile behavior are introduced and compared in different diagrams. Some alternative formulations of these criteria are discussed. At third, the formulation principles for the criteria are presented. In the main part, pressure-insensitive and pressure-sensitive criteria are separated. Some criteria, which contain a number of convex forms in the p-plane, are recommended for applications. In the case of partly not reliable measured data combined criteria with continuously differentiable transition can be used. Fitting methods based on mathematical, physical, and geometrical objective functions are necessary. Finally, some tests for multi-axial stress states are introduced and evaluated. Reference measurements for five materials are given. Examples demonstrate the application of different approaches in modeling certain limit behaviors. In the summary, the most important criteria of the equivalent stress concept are resumed. Possible directions for development of the equivalent stress concept are shown in the outlook.