Dynamic shear band development in dipolar thermoviscoplastic materials

354 Abstract We study thermomechanical deformations of a viscoplastic body deformed in plane strain compression at a nominal strain-rate of 5000 sec~. We develop a material model in which the second order gradients of the velocity field are also included as kinematic variables and propose constitutive relations for the corresponding higher order stresses. This introduces a material characteristic length I, in addition to the viscous and thermal lengths, into the theory. It is shown that the computed results become mesh independent for l greater than a certain value. Also, the consideration of higher order velocity gradients has a stabilizing effect in the sense that the initiation of shear bands is delayed and their growth is slower as compared to that for nonpolar (l -0) materials.