Abstract
SummaryIn this paper, the onset of mechanical instability in time‐sensitive elasto‐viscoplastic solids is theoretically analyzed at the constitutive level and associated with the occurrence of ‘spontaneous accelerations’ under stationary external perturbations. For this purpose, a second‐order form of Perzyna's constitutive equations is first derived by time differentiation, and a sufficient stability condition is identified for general mixed loading programs. These loading conditions are in fact the most general in both laboratory tests and real boundary value problems, where a combination of certain stress and strain components is known/prescribed.The theoretical analysis leads to find precise stability limits in terms of material hardening modulus. In the case of constitutive relationships with isotropic strain‐hardening, no instabilities are possible while the hardening modulus is larger than the so‐called ‘controllability modulus’ defined for (inviscid) elasto‐plastic materials. It is also shown that the current stress/strain rate may also directly influence the occurrence of elasto‐viscoplastic instability, which is at variance with elasto‐plastic inviscid media. Copyright © 2015 John Wiley & Sons, Ltd.
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