A generalization of the double-shearing model for plane-strain deformation to include an effect of viscosity

Abstract

A generalization of the double-shearing model for plane-strain deformation to include an effect of viscosity on the response of material to deformation is proposed. An asymptotic analysis of the system of equations in the vicinity of maximum friction surfaces is carried out. It is shown that there are dependencies of the cohesion on the equivalent strain rate, which lead to the same asymptotic behavior of the solutions based on the new model as that based on the original double-shearing model. It is proposed to adopt such dependencies in applications because they ensure a sufficiently smooth transition from the solutions based on the double-shearing model to those based on the new model. However, in this case the velocity field is singular, and therefore this fact should be taken into account while developing numerical codes.