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Conceptual Difficulties in Plasticity including the Gradient of one Scalar Plastic Field Variable
Author(s) -
Wulfinghoff Stephan,
Bayerschen Eric,
Böhlke Thomas
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410146
Subject(s) - plasticity , scalar field , laplace operator , scalar (mathematics) , variable (mathematics) , field (mathematics) , mathematics , classical mechanics , mathematical analysis , physics , geometry , thermodynamics , pure mathematics
This article discusses a conceptual problem of gradient plasticity theories including a scalar plastic field variable, the Laplacian of which enters the yield criterion. Since the plastic field variable is assumed a scalar, it contains no information on the direction of the plastic flow. The work at hand demonstrates that even arbitrarily small perturbations can determine the direction of the plastic deformation in many formulations, which is considered an unphysical behavior. In this sense, the solution is not stable with respect to the boundary conditions. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)