On the stability of strain-rate dependent solids. I - Structural examples

A linear stability criterion for strain-rate sensitive solids and structures is proposed and validated with help of two versions of Shanley's column, the first with two discrete supports and the second with a continuous distribution of supports. Linear stability transition is defined by the change in sign of the second derivative with respect to time of the columns angular position evaluated at the onset of perturbation. Results are validated by comparing its predictions with the outcome of nonlinear perturbation analysis and of imperfection sensitivity studies. It is shown that an imperfection evolves according to the stability predictions as long as the relative difference between the irreversible displacements of the supports can be disregarded.