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Scaling relation for low energy states in a single‐slip model in finite crystal plasticity
Author(s) -
Schubert T.
Publication year - 2015
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201300213
Subject(s) - infimum and supremum , scaling , slip (aerodynamics) , physics , plasticity , statistical physics , crystal plasticity , geometry , mathematics , mechanics , mathematical analysis , thermodynamics
We derive a scaling‐relation, for the infimum of the energy for small ϵ,δ > 0, where p, q ≥ 1, u: Ω → ℝ 2 is a deformation with suitable affine boundary conditions and γ: Ω → ℝ is a suitable slip variable. This model is motivated by a two‐dimensional single‐slip model in finite crystal plasticity. We show, that the infimum of the energy J ϵ,δ scales as . This scaling‐relation is attained by an asymptotically self‐similar branching construction.