A plot of the frequency-dependent wave propagation velocity for the case study problem with an overlocal plasticity model, with the elastic and local hardening wave speeds shown for reference (left). Stress histories using an overlocal plasticity model with a nonlocal length scale of 1m and a mesh resolution of 0.125m (right)

The following series of three articles (with common authors J. Burghardt and R. Brannon of the University of Utah) describes a state of insufficient experimental validation of conventional formulations of nonassociative plasticity (AKA nonassociated and non-normality).  This work provides a confirmation that such models theoretically admit negative net work in closed strain cycles, but this simple prediction has never been validated or disproved in the laboratory!

1. An early (mostly failed) attempt at experimental investigation of unvalidated plasticity assumptions (click to view),
2. A simple case study confirming that nonassociativity can cause non-unique and unstable solutions to wave motion problems (click to view),
3. An extensive study showing that features like rate dependence, hardening, etc. do not eliminate the instability and also showing that it is NOT related to conventional localization (click to view).

The possibility of liberation of energy in even infinitesimal perturbations leads to the never-validated attribute of a plastic wave speed exceeding that of the elastic precursor wave and consequently resulting in both nonuniqueness and a weak instability of ANY nonassociative plasticity model.

As pointed out in the above-cited articles, the so-called achronic instability is NOT related to the more common localization phenomenon associated with reaching a zero wave speed.  To date, there has been no compelling laboratory evidence showing whether or not the achronic instability is real or merely the byproduct of constitutive formulations that have been tuned to match conventional axisymmetric compression parameterization data just fine without adequate validation of those models for other loading modes.

Come on, plasticity community: let’s get this question of model trustworthiness resolved. The possibility of ill-posed and unstable governing equations for dynamic nonassociative plasticity wave motion has been recognized as far back as the 1940s, yet it continues to be relatively unknown by contemporary constitutive modelers (and often even disputed with grossly flawed logic). Let’s work on this problem.  It is fascinating because, as explained in the above-cited articles, a thorough experimental investigation has a Heisenberg-like uncertainty caused by an inability to measure a complete tangent stiffness tensor in the laboratory (the act of measuring some components of the tensor irreversibly alters the material to make it literally impossible to determine the other components with certainty); accordingly, a good analysis of the problem requires some level of mesoscale simulations (where it actually is possible to “reset” the material microstructure).