Bingham’s model

Since elements in Bingham s model are parallel to each other, their strains are identical, and the stresses are additive. The shear stress in Coulomb s element can not exceed the critical value, x Consequently, the strain rate generated by viscous element, should be proportional to the difference between the acting stress and the critical shear stress, namely ... 

When x < x, deformation does not occur (Fig. IX-14). Since the parameter of Bingham s model, r B, defines the derivative, dx/dy=r B, this constant value is referred to as the differential viscosity, in contrast to a variable effective viscosity, x/y = r ef (y). 

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