Incremental work minimization algorithm for rate-independent plasticity of single crystals

Summary A new constitutive algorithm for the rate‐independent crystal plasticity is presented. It is based on asymptotically exact formulation of the set of constitutive equations and inequalities as a minimum problem for the incremental work expressed by a quadratic function of non‐negative crystal...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2015-10, Vol.104 (3), p.157-184
Main Authors: Petryk, H., Kursa, M.
Format: Article
Language:English
Subjects:
Algorithms
Asymptotic properties
augmented Lagrangian method
Constraints
crystal plasticity
Crystals
incremental energy minimization
material stability
Mathematical models
Minimization
Optimization
rate-independent constitutive equations
Slip
solids
Tensile tests
variational methods
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Summary:Summary A new constitutive algorithm for the rate‐independent crystal plasticity is presented. It is based on asymptotically exact formulation of the set of constitutive equations and inequalities as a minimum problem for the incremental work expressed by a quadratic function of non‐negative crystallographic slips. This approach requires selective symmetrization of the slip‐system interaction matrix restricted to active slip‐systems, while the latent hardening rule for inactive slip‐systems is arbitrary. The active slip‐system set and incremental slips are determined by finding a constrained minimum point of the incremental work. The solutions not associated with a local minimum of the incremental work are automatically eliminated in accord with the energy criterion of path stability. The augmented Lagrangian method is applied to convert the constrained minimization problem to a smooth unconstrained one. Effectiveness of the algorithm is demonstrated by the large deformation examples of simple shear of a face‐centered cubic (fcc) crystal and rolling texture in a polycrystal. The algorithm is extended to partial kinematic constraints and applied to a uniaxial tension test in a high‐symmetry direction, showing the ability of the algorithm to cope with the non‐uniqueness problem and to generate experimentally observable solutions with a reduced number of active slip‐systems. Copyright © 2015 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4925