Granular Matter

, 18:34 | Cite as

Ordering and stress transmission in packings of straight and curved spherocylinders

  • G. Lu
  • R. C. Hidalgo
  • J. R. Third
  • C. R. Müller
Original Paper


In this work we apply the discrete element method (DEM) to model packings of spherocylinders. The so-called composite spheres method was used to construct particles of different aspect ratio, surface shape and curvature. Using the DEM we probe in detail the effect of particle curvature and surface shape on packing morphology and stress transmission. We find that particle shape has a remarkable influence on both the packing morphology (quantified via the solid fraction, particle orientation distribution and radial distribution function) and stress transmission. Specifically, elongated particles have a high preference for horizontal alignment, whereas an increasing particle curvature leads to a more continuous (i.e. less discrete) particle orientation distribution. Generally, we observe that rough and curved particles have a stronger tendency for interlocking (in particular for small particle aspect ratios, i.e. \(AR=2\) and 3) leading to the formation of dense packing structures. In addition packings of rough and curved particles of small aspect ratios favor stress transmission in the gravitational direction, thus, limiting stress saturation with depth.


Particle packing Non-spherical particles Particle ordering Stress transmission Discrete element method (DEM) 

List of symbols


Particle cross-sectional area (m\(^{2})\)


Particle aspect ratio (\(-\))

\(d_p \)

Primary sphere diameter (m)


Time step of DEM simulations (s)

\(E_k \)

Kinetic energy (J)

\(E_p \)

Elastic potential energy (J)

\(f_{ij} \)

Contact force between particles i and j (N)

\(F_n \)

Normal force (N)

\(F_t \)

Tangential force (N)

\(G\left( r \right) \)

Radial distribution function (\(-\))


Dimensionless packing depth (\(-\))

\(h_c \)

Characteristic depth of packing (\(-\))


Height of container (m)

\(k_n \)

Normal spring stiffness (N/m)

\(k_t \)

Tangential spring stiffness (N/m)

\(l_{axial} \)

Length of particle major axis (m)


Particle mass (kg)


Number of particles (\(-\))

\(P_0 \)

Stress (N/m)

\(P_j \)

Saturation stress (N/m)


Distance/vector relative to a point (m)

\(\delta r\)

Differential distance (m)

\(v_n \)

Relative normal velocity (m/s)

\(v_t \)

Relative tangential velocity (m/s)


Width of container (m)


Coordinates (m)

Greek letters

\(\delta _n \)

Particle overlap (m)

\(\delta _t \)

Tangential displacement (m)

\(\eta _n \)

Normal damping factor (\(-\))

\(\eta _t \)

Tangential damping factor (\(-\))

\(\gamma \)

Particle orientation angle (\(^{\circ })\)

\(\mu \)

Coefficient of friction (\(-\))

\(\phi \)

Solid fraction (\(-\))

\(\rho \)

Number of particles per unit area (1/m\(^{2})\)

\(\rho _p \)

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

\(\theta \)

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

\(\omega \)

Coarse-graining scale (\(-\))

\(\sigma _v \)

Major eigenvalue of stress tensor (N/m)

\(\sigma _h \)

Minor eigenvalue of stress tensor (N/m)

\(\bar{\sigma }_{\alpha \beta } \left( \mathbf{r} \right) \)

Mean stress tensor (N/m)

\(\varphi \left( \mathbf{r} \right) \)

Gaussian coarse-graining function (1/m\(^{2})\)



The authors are grateful to the Swiss National Science Foundation (200021_132657/1) and the China Scholarship Council (Guang Lu) for partial financial support of this work. R.C. Hidalgo acknowledges the financial support from Ministerio de Economía y Competitividad (Spanish Government) through FIS2011-26675 and FIS2014-57325 Projects.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • G. Lu
    • 1
  • R. C. Hidalgo
    • 2
  • J. R. Third
    • 1
  • C. R. Müller
    • 1
  1. 1.Department of Mechanical and Process Engineering, Institute of Energy TechnologyETH ZürichZürichSwitzerland
  2. 2.Departamento de Física, Facultad de CienciasUniversidad de NavarraPamplonaSpain

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