BinghamModellen

Binghammodellen, commonly referred to as the Bingham model or Bingham plastic, is a simple rheological constitutive model used to describe viscoplastic materials. It postulates that such materials behave as rigid bodies under small applied stresses and begin to flow only when the shear stress exceeds a finite yield value. Once yielding occurs, the material flows with a constant viscosity, and the shear rate increases linearly with the excess stress.

The constitutive relation of the Bingham model can be written as a piecewise description: the shear rate gamma_dot is zero when the shear stress tau is less than or equal to the yield stress tau_y; when tau exceeds tau_y, the relation tau = tau_y + mu_p * gamma_dot holds, where mu_p is the plastic (zero-shear) viscosity. Equivalently, gamma_dot = (tau - tau_y) / mu_p for tau > tau_y. The model is frequently used in terms of materials such as pastes, gels, suspensions, and drilling muds.

Applications of Binghammodellen span civil engineering, food science, cosmetics, and process industries, where materials exhibit a yield stress and flow only after yielding. The model offers a straightforward framework for numerical simulation and analytical work, especially in laminar flow problems and simple geometries.

Limitations include its inability to capture shear-thinning or shear-thickening behavior, time-dependent effects, and thixotropy observed in many real materials. More advanced models, such as the Herschel-Bulkley family, generalize the Bingham framework by incorporating a nonlinear dependence on shear rate.