Shear localisation during deformation of reactive thermo-visco-elastic-plastic materials

A one-dimensional model for the initiation of shear bands in a reactive material is developed, with an Arrhenius source term to model the chemical reaction occurring in the band. An inhomogeneity in the heat flux is used as the stimulus for localised plastic deformation, and the problem is treated as a perturbation to the elastic solution. In the analysis, the thin zone of localisation is identified as a boundary layer. It is found that the behaviour of the perturbations to the temperature and stress in the band are governed by three dimensionless parameters which are known in terms of various material properties. The resulting equations are solved numerically and a criterion for the onset of shear banding is discussed.