INSTABILITY IN SIMPLE SHEAR DEFORMATIONS OF STRAIN-SOFTENING MATERIALS

A quasistatic stability analysis is performed for the problem of a strain-softening material undergoing dynamic one-dimensional simple shear. This analysis is basically algebraic in nature and deals strictly with the underlying linearized problem. A simple algebraic criterion for the onset of instability is developed. An application of the criterion to two steels is then made and compared with experimental data, and qualitative agreement is observed. The analysis is then refined in a special case to include the time-dependence of the underlying parallel flow in the stability method. For a simple constitutive assumption (that of a thermoviscous material), it is found that the refined analysis can yield a somewhat different stability criterion than the quasistatic analysis. The importance of this for the problem under consideration is also discussed.