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Some theoretical and computational aspects of single‐crystal strain‐gradient plasticity
Author(s) -
Reddy B.D.
Publication year - 2013
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.201200101
Subject(s) - dissipative system , viscoplasticity , finite strain theory , plasticity , dissipation , finite element method , convergence (economics) , context (archaeology) , deformation (meteorology) , work (physics) , mathematics , range (aeronautics) , minification , mathematical optimization , physics , materials science , constitutive equation , geology , thermodynamics , paleontology , meteorology , economics , composite material , economic growth
Variational formulations are constructed for rate‐independent problems in single‐crystal strain‐gradient plasticity. The framework makes use of the flow rule expressed in terms of a dissipation function. The formulation extends to the finite‐deformation context earlier work on this problem. Provision is made for energetic and dissipative microstresses, and a range of defect energies is accounted for. The minimization problem corresponding to the time‐discrete formulation is derived. Two special cases are then treated: first, for the small‐strain problem with energetic microstresses, results on well‐posedness, convergence of finite element approximations, the associated algorithms, and computational examples, are discussed. Secondly, recent computational work on the the related large‐deformation viscoplastic problem, with both energetic and dissipative effects, is presented and discussed for problems involving ensembles of grains.