Bingham

{

    "materials": [
        {
            "id": 0,
            "type": "Bingham2D",
            "density": 2000,
            "youngs_modulus": 100e6,
            "poisson_ratio": 0.3,
            "tau0": 200,
            "mu": 0.5,
            "critical_shear_rate": 1.0,
            "incompressible": false
        }
    ]

}

• "id" is the material ID corresponding to a subset (or all) of the generated material points.
• "type" is either "Bingham2D" or "Bingham3D".
• "density" is material density.
• "youngs_modulus" is the constant elastic parameter Young's modulus.
• "poisson_ratio" is the constant elastic parameter Poisson's ratio.
• "tau0" is the shear yield stress.
• "mu" is the constant plastic viscosity.
• "critical_shear_rate" is the critical yielding shear rate.
• "incompressible" flag is set true for incompressible materials.

Details of the constitutive equations for non-Newtonian fluids are provided in [1]. The general Bingham model is from [2].

References

[1] Reddy, J. N. (2014). An Introduction to Nonlinear Finite Element Analysis: with applications to heat transfer, fluid mechanics, and solid mechanics. OUP Oxford.

[2] Beverly, C. R. and Tanner, R. I. (1992). Numerical analysisof three-dimensional Bingham plastic flow. Journal of non-newtonian fluid mechanics 42(1-2), 85-115.