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A bond model for DEM simulation of cementitious materials and deformable structures

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Abstract

There is an increasing use of the discrete element method (DEM) to study cemented (e.g. concrete and rocks) and sintered particulate materials. The chief advantage of the DEM over continuum based techniques is that it does not make assumptions about how cracking and fragmentation initiate and propagate, since the DEM system is naturally discontinuous. The ability for the DEM to produce a realistic representation of a cemented granular material depends largely on the implementation of an inter-particle bonded contact model. This paper presents a new bonded contact model based on the Timoshenko beam theory which considers axial, shear and bending behaviour of the bond. The bond model was first verified by simulating both the bending and dynamic response of a simply supported beam. The loading response of a concrete cylinder was then investigated and compared with the Eurocode equation prediction. The results show significant potential for the new model to produce satisfactory predictions for cementitious materials. A unique feature of this model is that it can also be used to accurately represent many deformable structures such as frames and shells, so that both particles and structures or deformable boundaries can be described in the same DEM framework.

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Abbreviations

\(A\) :

Area \((\hbox {m}^{2})\)

\(d\) :

Translational displacement (m)

\(e\) :

Coefficient of restitution

\(E\) :

Young’s modulus (Pa)

\(f_{s}\) :

Form factor for shear

\(G\) :

Shear modulus (Pa)

\(I\) :

Second moment of area \((\hbox {m}^{4})\)

\(K\) :

Stiffness \((\hbox {N m}^{-1})\)

\(L\) :

Length (m)

\(m\) :

Mass (kg)

\(M\) :

Moment (N m)

\(N\) :

Random number

\(P\) :

Position

\(r\) :

Radius (m)

\(S\) :

Mean bond strength (Pa)

\(t\) :

Time (s)

\(u\) :

Displacement vector (m)

\(W\) :

Point load (N)

\(x, y, z\) :

Local Cartesian coordinates (m, m, m)

\(X, Y, Z\) :

Global Cartesian coordinates (m, m, m)

\(\gamma \) :

Transformation matrix

\(\delta \) :

Mid-span deflection (m)

\(\Delta \)t:

Time step (s)

\(\varepsilon \) :

Strain

\(\eta \) :

Contact radius multiplier

\(\lambda \) :

Bond radius multiplier

\(\mu \) :

Coefficient of friction

\(\rho \) :

Density \((\hbox {kg m}^{-3})\)

\(\varsigma \) :

Coefficient of variation of strength

\(\sigma \) :

Axial stress (MPa)

\(\tau \) :

Shear stress (Pa)

\(v\) :

Poisson’s ratio

\(\alpha , \beta \) :

Ends of a single bond

\(A, B\) :

Particle labels

\(b\) :

Bond

\(c\) :

Bulk

\(C\) :

Compressive stress

crit :

Critical

\(g\) :

Geometry

min:

Minimum

max:

Maximum

\(\rho \) :

Particle

\(r\) :

Rolling friction

\(s\) :

Static friction

\(S\) :

Shear stress

\(T\) :

Tensile stress

\(x, y, z\) :

Local Cartesian coordinates

\(X, Y, Z\) :

Global Cartesian coordinates

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Acknowledgments

The authors would like to thank EPSRC and DEM Solutions Ltd for the funding and sponsorship. We are also grateful for the assistance and discussion with DEM solutions.

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Authors and Affiliations

  1. Institute for Infrastructure and Environment, School ofEngineering, The University of Edinburgh, The King’s Buildings, Edinburgh, EH9 3JL, Scotland, UK

    Nicholas J. Brown & Jin Y. Ooi

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

    Jian-Fei Chen

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  1. Nicholas J. Brown
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Correspondence to Jin Y. Ooi.

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Brown, N.J., Chen, JF. & Ooi, J.Y. A bond model for DEM simulation of cementitious materials and deformable structures. Granular Matter 16, 299–311 (2014). https://doi.org/10.1007/s10035-014-0494-4

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  • DOI: https://doi.org/10.1007/s10035-014-0494-4

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