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

摘要

A linear stability criterion for strain-rate sensitive solids and structures is proposed and validated with the 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 column's angular position evaluated at the onset of perturbation. This criterion pertains to the initiation of instabilities but is not expected to provide information on their Iong term development. Two parameters influence linear stability: the dimensionless number T, defined as the ratio of the relaxation time of the viscous support to the characteristic loading time, and the perturbation size. It is found that the critical load of principal equilibria, defined for a straight column and a zero value of T, is the classical reduced modulus load, in agreement with existing stability criteria for rate-independent models based on maximum dissipation. For arbitrary values of T, two critical loads are identified at the linear stability transition. The first is named the rate- dependent tangent modulus load and is valid for perturbations sufficiently small to prevent initial unloading. That load coincides with the classical tangent modulus load for T tending to zero and is, surprisingly. a decreasing function of that dimensionless number. The second critical load is termed the rate-dependent reduced modulus load, and is applicable to columns that are partly unloaded at the onset of perturbation. This critical load approa