Stability and imperfections in quasistatic wiscopiastic solutions

The effect of imperfections on the structure of shear bands in strain-softening viscoplasticity is studied via a closed form solution. The stability of various solutions is then examined by varying the data through imperfections. It is shown that a step-function imperfection, such as commonly used in finite element solutions, leads to a step-function shear strain field, which is an unstable solution. Arbitrary C⁰ and C¹ imperfections lead to C^0> and C¹ strain fields, respectively. Fourier analyses show that the imperfection scales the response of the viscoplastic material: the Fourier spectrum of the strain field is strongly influenced by the Fourier spectrum of the imperfection.