Plasticity as the Γ‐limit of a Nonlinear Dislocation Energy with Mixed Growth | Zendy

Ginster Janusz | Zendy

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Plasticity as the Γ‐limit of a Nonlinear Dislocation Energy with Mixed Growth

Author(s) -

Ginster Janusz

Publication year - 2015

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.201510262

Subject(s) - curl (programming language) , plasticity , nonlinear system , rigidity (electromagnetism) , mathematical analysis , dislocation , balanced flow , mathematics , elastic energy , convergence (economics) , limit (mathematics) , rotation (mathematics) , classical mechanics , geometry , physics , computer science , condensed matter physics , quantum mechanics , thermodynamics , economic growth , economics , programming language

We consider a model for straight parallel edge dislocations with a nonlinear elastic energy with mixed growth. By means of Γ‐convergence we show that the suitably rescaled energy converges to a strain‐gradient plasticity model. As a tool we proof a generalized rigidity estimate which bounds the distance of a field with non‐vanishing curl to a specific rotation by the distance to all rotations. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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