The CSM group has independently confirmed a case study demonstrating the truth of a claim in the literature that any non-associative rate-independent model admits a non-physical dynamic achronistity instability. By stimulating a non-associative material in the “Sandler-Rubin wedge” (above yield but below the flow surface), plastic waves are generated that travel faster than elastic waves, thus introducing a negative net work in a closed strain cycle that essentially feeds energy into a propagating wave to produce unbounded increases in displacement with time.
The influence of various advanced and/or nonclassical plasticity features (hardening, rate dependence, irregular flow rules, nonlocal theory) has been thoroughly investigated. Of these, only an irregular flow rule (which essentially shuts down the Sander-Rubin wedge by allowing the plastic strain rate direction to be affected by the total strain rate direction) has been found to eliminate the instability. However, no experimental evidence has ever emerged to support the irregular flow rule for the class of materials of interest; moreover, some mesoscale investigations suggest that an irregular flow rule might exist but not in the axisymmetric loading of the case study. Thus, validated model features capable of eliminating the Sander-Rubin instability continue to be an area for further research.
Jeff Burghardt (PhD student, Mech. Engr., UofU)
Tom Pučik (independent consultant, deceased)