Vol. 10, No. 2, 2015

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Nonuniqueness and instability of classical formulations of nonassociated plasticity, II: Effect of nontraditional plasticity features on the Sandler–Rubin instability

Jeffrey Burghardt and Rebecca M. Brannon

Vol. 10 (2015), No. 2, 149–166

In the companion article a case study problem was presented that illustrated a dynamic instability related to nonassociated plastic flow. This instability allows stress waves to grow in both amplitude and width as they propagate. In addition to this physically implausible behavior, multiple solutions to the equations of motion were shown to exist, which causes numerical solutions not to converge with mesh refinement. Reformulation of some aspects of traditional plasticity theory is necessary since associated models over-predict the amount of plastic dilatation, and nonassociated models may result in this physically unrealistic behavior. The case study solutions in the companion paper were limited to a few relatively simple plastic models. The purpose of this paper is to investigate the effects of various traditional and nontraditional plasticity features on the existence of the instability and resulting nonuniqueness. The instability and nonuniqueness are shown to persist with both hardening and softening. An incrementally nonlinear model is shown to eliminate the instability and result in mesh-independent solutions. A viscoplastic model is shown to lead to unstable solutions for all loading rates. However, mesh-independent numerical solutions are found when the loading timescale is much less than the plastic relaxation time. A nonlocal plasticity model is shown to produce solutions that are both unstable and mesh-dependent. Therefore, of the models considered, only the incrementally nonlinear model was capable of eliminating this nonphysical instability. This work provides much needed direction for laboratory investigations of the validity of incrementally nonlinear flow rules.

plasticity, flow rule, nonassociated flow rule, instability, incremental nonlinearity
Received: 2 July 2014
Revised: 15 March 2015
Accepted: 4 April 2015
Published: 5 August 2015
Jeffrey Burghardt
1935 S. Fremont Dr.
Salt Lake City, UT 84104
United States
Rebecca M. Brannon
University of Utah
50 S. Campus Dr.
Salt Lake City, UT 84108
United States