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01.Evolution Equations for Grain Growth and Coarsening (pp.5-60)
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A Variational Alternative to the Use of Condensed Energy in Crystal Plasticity Based on the Evolution of Microstructure History (pp.363-372) $100.00
Authors:  (D. M. Kochmann, K. Hackl, Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, California, USA, and others)
Abstract:
The study of the origin and evolution of microstructures in crystalline solids has
gained much interest, virtue of the essential influence of such microscale structures
on the macroscopic mechanical properties of the material. The formation of regular,
fine-scale patterns on the materialís microlevel has been reasoned to stem from non-
(quasi)convex energy potentials, which result in a lack of homogeneous solution states
to the underlying thermodynamic extremum principles of minimum potential energy
and maximum dissipation. The theory of relaxation has provided beneficial tools for
understanding and analyzing the origin and subsequent development of microstructures
in finite-strain plasticity models, whose prediction and simulation is commonly
based on condensed potentials to overcome the non-(quasi)convexity and to render
the problem well-posed while considering all admissible microfluctuations, i.e., microstructures.
We outline an incremental variational alternative to the application of
condensed potentials, which allows to account for more physical insight and which
greatly expands the regime of applicability of material models. Also, we illustrate
the incremental approach by its application to an incompressible Neo-Hookean solid
with one and multiple active slip systems, but the method can readily be generalized
to problems of microstructure evolution. 


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A Variational Alternative to the Use of Condensed Energy in Crystal Plasticity Based on the Evolution of Microstructure History (pp.363-372)