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Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model

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Abstract

An adhesive elasto-plastic contact model for the discrete element method with three dimensional non-spherical particles is proposed and investigated to achieve quantitative prediction of cohesive powder flowability. Simulations have been performed for uniaxial consolidation followed by unconfined compression to failure using this model. The model has been shown to be capable of predicting the experimental flow function (unconfined compressive strength vs. the prior consolidation stress) for a limestone powder which has been selected as a reference solid in the Europe wide PARDEM research network. Contact plasticity in the model is shown to affect the flowability significantly and is thus essential for producing satisfactory computations of the behaviour of a cohesive granular material. The model predicts a linear relationship between a normalized unconfined compressive strength and the product of coordination number and solid fraction. This linear relationship is in line with the Rumpf model for the tensile strength of particulate agglomerate. Even when the contact adhesion is forced to remain constant, the increasing unconfined strength arising from stress consolidation is still predicted, which has its origin in the contact plasticity leading to microstructural evolution of the coordination number. The filled porosity is predicted to increase as the contact adhesion increases. Under confined compression, the porosity reduces more gradually for the load-dependent adhesion compared to constant adhesion. It was found that the contribution of adhesive force to the limiting friction has a significant effect on the bulk unconfined strength. The results provide new insights and propose a micromechanical based measure for characterising the strength and flowability of cohesive granular materials.

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Abbreviations

\(\mathrm d \) :

Particle diameter (m)

\(d_{avg}\) :

Average particle diameter (m)

\(e\) :

Co-efficient of restitution

\(g\) :

Gravitational constant \((\hbox {m/s}^{2})\)

\(m^{*}\) :

Equivalent mass of the particles (kg)

\(N\) :

Number of particles

\(n\) :

Non-linear index parameter

\(P\) :

Pressure (kPa)

u :

Unit normal vector

\(Z\) :

Coordination number at peak

Zi :

Instantaneous coordination number

\(F_{at}\) :

Average adhesive strength at contact (N)

\(f_{0}\) :

Constant adhesive strength at first contact (N)

\(f_{\mathrm{t}}\) :

Contact tangential force (N)

\(f_{\mathrm{ct}}\) :

Coulomb limiting tangential force (N)

\(f_{\mathrm{nd}}\) :

Normal dam** force (N)

\(f_{i}^{c}\) :

Contact force (N)

\(f_{atp}\) :

Average tensile force at the peak (N)

\(f_{\mathrm{ts}}\) :

Tangential spring force (N)

\(f_{\mathrm{td}}\) :

Tangential dam** force (N)

\(f_{\mathrm{hys}}\) :

Hysteretic spring force (N)

\(f_{\mathrm{ts(n-1)}}\) :

Tangential spring force at previous time step (N)

\(I_{i}\) :

Moment of inertia \((\hbox {m}^{4})\)

\(l_{i}^{c}\) :

Vector from centre of particle to the contact point

\(k_{1}\) :

Loading stiffness parameter (kN/m)

\(k_{2}\) :

Unloading/reloading stiffness parameter (kN/m)

\(k_{\mathrm{adh}}\) :

Adhesive stiffness parameter (kN/m)

\(k_{\mathrm{t}}\) :

Tangential stiffness (kN/m)

\(\varvec{\nu }_{\mathbf{t}}\) :

Relative tangential velocity (m/s)

\(\nu _{\mathrm{n}}\) :

Magnitude of relative normal velocity (m/s)

\(\upsigma _{\mathrm{u}}\) :

Unconfined yield strength (kPa)

\(\upsigma _{\mathrm{a}}\) :

Axial stress (kPa)

\(\upsigma _{\mathrm{t}}\) :

Bulk tensile strength (kPa)

\(\sigma _{1}\) :

Axial consolidation stress (kPa)

\(\rho \) :

Particle density \((\hbox {kg/m}^{3})\)

\(\upvarepsilon \) :

Total bulk deformation

\(\upvarepsilon _{\mathrm{a}}\) :

Bulk axial strain

\(\upvarepsilon _{\mathrm{p}}\) :

Total plastic deformation

\(\beta _{\mathrm{n}}\) :

Normal dashpot co-efficient

\(\beta _{\mathrm{t}}\) :

Tangential dashpot coefficient

\(\phi \) :

Angle of friction \((^{\circ })\)

\(\Delta f_{\mathrm{ts}}\) :

Incremental tangential force (N)

\(\delta \) :

Total normal overlap (m)

\(\delta _{\max }\) :

Maximum normal overlap (m)

\(\delta _{\mathrm{p}}\) :

Plastic overlap (m)

\(\upeta \) :

Sample bulk porosity

\(\upeta _{\mathrm{c}}\) :

Consolidated bulk porosity

\(\upeta _{\mathrm{f}}\) :

Fill porosity

\(\mu \) :

Co-efficient of friction

\(\mu _{\mathrm{r}}\) :

Coefficient of rolling friction

\(\tau _{i}\) :

Total applied torque (N m)

\(\omega _{i}\) :

Unit angular velocity vector (radian/s)

\(\uplambda _{p}\) :

Contact plasticity

\(\lambda _{b}\) :

Bulk plasticity

\(\dot{\gamma }\) :

Shear rate

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Acknowledgments

The support of the European Commission under the Marie Curie Initial Training Network for the PARDEM Project is gratefully acknowledged. The authors would also like to thank Prof. Stefan Luding and Dr. Hossein Ahmadian for useful discussions.

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Authors and Affiliations

  1. School of Engineering, The University of Edinburgh, King’s Buildings, Edinburgh, EH9 3JL, Scotland, UK

    Subhash C. Thakur, John P. Morrissey, ** Sun & ** Y. Ooi

  2. School of Planning, Architecture and Civil Engineering, Queen’s University Belfast, Belfast, BT9 5AG, Northern Ireland, UK

    J. F. Chen

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  1. Subhash C. Thakur
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Thakur, S.C., Morrissey, J.P., Sun, J. et al. Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model. Granular Matter 16, 383–400 (2014). https://doi.org/10.1007/s10035-014-0506-4

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