Non-convex rate dependent strain gradient crystal plasticity and deformation patterning

Yalçinkaya T., Brekelmans W., Geers M.

International Journal of Solids and Structures, vol.49, no.18, pp.2625-2636, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 18
  • Publication Date: 2012
  • Doi Number: 10.1016/j.ijsolstr.2012.05.029
  • Journal Name: International Journal of Solids and Structures
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2625-2636
  • Keywords: Dislocation-microstructure, Patterning, Non-convexity, Strain gradient, Crystal plasticity, Localization, DISLOCATION-STRUCTURES, MICROSTRUCTURE EVOLUTION, TEM OBSERVATIONS, PATH CHANGES, ENERGY, MODEL, STEEL, EQUILIBRIUM, BEHAVIOR, STRESS
  • Middle East Technical University Affiliated: No


A rate dependent strain gradient crystal plasticity framework is presented where the displacement and the plastic slip fields are considered as primary variables. These coupled fields are determined on a global level by solving simultaneously the linear momentum balance and the slip evolution equation, which is derived in a thermodynamically consistent manner. The formulation is based on the 1D theory presented in Yalcinkaya et al. (2011), where the patterning of plastic slip is obtained in a system with non-convex energetic hardening through a phenomenological double-well plastic potential. In the current multi-dimensional multi-slip analysis the non-convexity enters the framework through a latent hardening potential presented in Ortiz and Repettto (1999) where the microstructure evolution is obtained explicitly via a lamination procedure. The current study aims the implicit evolution of deformation patterns due to the incorporated physically based non-convex potential. © 2012 Elsevier Ltd. All rights reserved.