A phenomenological, polycrystalline version of a nonlocal crystal plasticity model is formulated. The presence of geometrically necessary dislocations (GNDs) at, or near, grain boundaries is modeled as elastic lattice curvature through a curl of the elastic part of the deformation gradient. This spatial gradient of an internal state variable introduces a length scale, turning the local form of the model, an ordinary differential equation (ODE), into a nonlocal form, a partial differential equation (PDE) requiring boundary conditions. Small lattice elastic stretching results from the presence of dislocations and from macroscopic external loading. Finite deformation results from large plastic slip and large rotations. The thermodynamics and constitutive assumptions are written in the intermediate configuration in order to place the plasticity equations in the proper configuration for finite deformation analysis.
A Nonlocal Phenomenological Anisotropic Finite Deformation Plasticity Model Accounting for Dislocation Defects
Contributed by the Materials Division for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received by the Materials Division September 7, 2001; revised manuscript received March 15, 2002. Guest Editors: Tariq A. Khraishi and Hussein M. Zbib.
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Regueiro, R. A., Bammann , D. J., Marin, E. B., and Garikipati, K. (June 10, 2002). "A Nonlocal Phenomenological Anisotropic Finite Deformation Plasticity Model Accounting for Dislocation Defects ." ASME. J. Eng. Mater. Technol. July 2002; 124(3): 380–387. https://doi.org/10.1115/1.1480410
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