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A variational alternative to the use of condensed energy in crystal plasticity based on the evolution of microstructure history
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 material's 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. © 2012 No+va Science Publishers, Inc. All rights reserved.