Bingham - geomechanics/mpm GitHub Wiki

{

    "materials": [
        {
            "id": 0,
            "type": "Bingham2D",
            "density": 2000,
            "youngs_modulus": 100e6,
            "poisson_ratio": 0.3,
            "volumetric_gamma": 7.0,
            "tau0": 200,
            "dynamic_viscosity": 0.5,
            "regularization_parameter": 10,
            "flocculation_state": 0.5,
            "flocculation_parameter": 1.0,
            "deflocculation_rate": 1.0
        }
    ]

}

• "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.
• "volumetric_gamma" is a constant used in the equation of state to compute pressure.
• "tau0" is the shear yield stress.
• "dynamic_viscosity" is the constant plastic viscosity.
• "regularization_parameter" is the Papanastasiou regularization parameter.
• "flocculation_state" is the initial internal structural state of the material.
• "flocculation_parameter" is the flocculation rate in the unit of (Pa/s).
• "deflocculation_rate" is the constant that governs the exponential decrease of shear stress under a constant shear rate.

Details of the constitutive equations for non-Newtonian fluids are provided in [1]. The general Bingham model is from [2]. The thixotropy Bingham model can be found in [3] and [4].

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.

[3] Wilkes, C., Kumar, K., & Biscontin, G. (2023). Investigating the thixotropic behaviour of Tremie Concrete using the Slump-flow test and the Material Point Method. Cement and Concrete Composites, 143, 105222.

[4] Yu, J., Chandra, B., Wilkes, C., Zhao, J., & Soga, K. (2025). An elasto-viscoplastic thixotropic model for fresh concrete capturing flow-rest transition. arXiv preprint arXiv:2512.23364.