Stress fields in plane irrotational flows of viscous and perfectly plastic continua

The viscous and viscoplastic stress fields in three families of plane irrotational flows are determined by using the properties of complex analytic functions. In these flows the slip line fields are defined by the continuation of an orthogonal pair of characteristics that are straight lines, logarithmic spirals or Cornu’s spirals, respectively. The three families of solutions comprise all plane flows which, when subjected to changes in the time scale, continue to satisfy the dynamical equations of a viscoplastic continuum in the sense of Bingham.