A nonlinear viscoplasticity theory for transversely isotropic materials

We formulate constitutive equations for a transversely isotropic viscoplastic material that is the analogue of a Bingham fluid for an isotropic material. The material is assumed to be incompressible and inextensible in the direction of the axis of transverse isotropy. A general yield criterion for transversely isotropic material is formulated. The rate-of-deformation is assumed to depend on the excess stress over the yield stress. Linear and nonlinear constitutive equations for the excess stress are established. The case in which the excess stress depends on higher order deformation rates is also considered.