Computational aspects in presence of negative strain-rate sensitivity with application to aluminium alloys exhibiting the Portevin–Le Chatelier effect

Loss of ellipticity of the time-discretized boundary-value problem for elastic–viscoplastic solid materials with negative strain-rate sensitivity (SRS) is studied. The physical mechanism responsible for the negative SRS is assumed to be dynamic strain ageing. For the time-discretized problem the negative SRS translates into softening and may possibly lead to loss of ellipticity when the time step is greater than a critical value. The paper provides a method to compute the critical time step and illustrates the results for an aluminium alloy