Rate-Dependent Nonlocal Crystal Plasticity: Implementation and Boundary Layers

Eduardo Bittencourt, Alan Needleman


A finite element implementation of a rate-dependent version of the nonlocal crystal plasticity theory of Gurtin (J Mech Phys Solids 50:5-32 (2002)) is presented. The algorithm used is equivalent to a conventional forward gradient method when the nonlocal terms are absent. Attention is restricted to small deformations so that geometry changes are neglected. A two dimensional analysis of simple shear of a constrained single crystal strip with two symmetric slip systems is carried out. The results are compared with results of the corresponding rate-independent theory. Boundary layers develop that give rise to size effects. For the rate sensitivity in the calculations here, it is found that the boundary layers are not as strongly dependent on the dissipative hardening as in the rate-independent case. In cases without dissipative hardening, the rate-dependent results essentially coincide with those of the
rate-independent theory for large characteristic lengths. However, for small characteristic lengths, rate effects can substantially change the boundary layers.

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