Summary
The paper presents some aspects of the formulation and numerical implementation of localization phenomena in elastoplastic solids at small strains. At first we point out the theoretical foundation and algorithmic implementation of a localpre-critical localization analysis for the detection of critical zones which may cause a loss of global structural stability, e.g. shear-bands. The second part proposes a particular approach to thepost-critical localization analysis in order to trace post-critical localized equilibrium branches of solids with a global displacement-discontinuity surface. Within this context we investigate two general constitutive approaches to the modelling of the displacement discontinuity and develop a finite-element formulation for its numerical implementation.
Übersicht
Die Arbeit stellt Aspekte der Formulierung und numerischen Implementation von Lokalisierungsphänomenen in elastoplastischen Festkörpern im Rahmen kleiner Verzerrungen dar. Zunächst diskutieren wir die theoretischen Grundlagen und die algorithmische Implementation einer lokalen begleitendenprä-kritischen Lokalisierungsanalysis zur Aufdeckung von kritischen Zonen wie Scherbändern, die den Verlust der globalen Strukturstabilität bewirken können. Der zeiite Teil schlägt einen besonderen Zugang zu einerpost-kritischen Lokalisierungsanalysis vor zur Verfolgung postkritischer lokalisierter Gleichgewichtspfade von Strukturen mit einer globalen Verschiebungsdiskontinuität. In diesem Zusammenhang untersuchen wir zwei allgemeine konstitutive Zugänge zur Modellierung der Verschiebungsdiskontinuität und entwickeln eine Finite-Elemente-Formulierung zu ihrer numerischen Implementation.
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Miehe, C., Schröder, J. Post-critical discontinuous localization analysis of small-strain softening elastoplastic solids. Arch. Appl. Mech. 64, 267–285 (1994). https://doi.org/10.1007/BF00789125
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DOI: https://doi.org/10.1007/BF00789125