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Application of DEM to predict the elastic behavior of particulate composite materials

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Abstract

The present paper deals with a novel method to predict the effective elastic behavior of heterogeneous continuous materials using discrete element method. This work uses a numerical approach based on a hybrid particulate-lattice model in which discrete elements are linked by cohesive forces through beam elements. Mechanical tests, carried out on particulate composite material, are performed in terms of effective elastic properties and stress fields which exhibit a good adequation with other numerical and analytical approaches such as the finite element method and the Fast Fourier Transform based method. As an example, the proposed approach is performed to predict the elastic properties of a ceramic/resin composite as well as the local effects by means of equivalent Von Mises stress.

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Abbreviations

\(\epsilon \) :

Imposed strain in tensile and shear tests

\(\nu _{M}\) :

Macroscopic Poisson’s ratio

\(\rho _\mu \) :

Microscopic mass density

\(\rho _M\) :

Macroscopic mass density

\(\sigma _{d}\) :

Deviatoric stress tensor

\(\sigma _{eq}\) :

Equivalent Von-Mises stress

\(\theta _{i}\) :

Rotation of particle i

\(\varepsilon _{rel}\) :

Relative error

\(A_{\mu }\) :

Cross-section of the beam

\(c_{r}\) :

Contrast of properties

D :

Diameter of cylindrical inclusions

D :

Diameter of the cylinders

\(d_{\alpha }\) :

Branch vector of contact \(\alpha \)

\(D_{Z}\) :

Variance parameter

E :

Effective Young’s modulus

\(E^{i}\) :

Young’s modulus of the inclusion phase

\(E^{m}\) :

Young’s modulus of the matrix phase

\(E_{\mu }\) :

Microscopic Young’s modulus

\(E_{M}\) :

Macroscopic Young’s modulus

\(F^{j \rightarrow i }\) :

Force of interaction of the particle j on the particle i

\(F_{i}^{ext}\) :

External force acting on particle i

G :

Effective shear modulus

\(I_{i}\) :

Quadratic moment of inertia of the particle i

\(k_n\) :

Normal stiffness parameter

\(k_t\) :

Tangential stiffness parameter

\(K_{V}^{i}\) :

Set of contacts in the specimen i of volume V

L :

Length of the pattern

L :

Length of the representative pattern

\(M^{j \rightarrow i }\) :

Moment of interaction of the particle j on the particle i

\(m_{i}\) :

Elementary mass of the particle i

\(M_{i}^{ext}\) :

External moment acting on particle i

\(n_{r}\) :

Number of realizations

\(R_i\) :

Radius of particle i

\(r_{\alpha }\) :

Reaction force of contact \(\alpha \)

\(r_{\mu }\) :

Dimensionless radius of the beam

\(u_{n}^{i}\) :

Normal displacement of particle i

\(u_{t}^{i}\) :

Tangential displacement of particle i

Z :

Investigated property

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Acknowledgments

The authors thank LMCPA (UVHC), SIRRIS, UMONS and INISMA-CRIBC (members of EMRA) for supplying the experimental data and the thermomechanical characterisation of the material.

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Authors and Affiliations

  1. Laboratoire des Technologies Innovantes, EA 3899, UPJV, IUT de l’Aisne, 48 rue d’Ostende, 02100, Saint Quentin, France

    H. Haddad, W. Leclerc, M. Guessasma, C. Pélegris & E. Bellenger

  2. Centre de Développement des Technologies Avancées, Cité 20 Aoôt 1956, B.P. 17, 16303, Baba-Hassen, Alger, Algeria

    N. Ferguen

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  1. H. Haddad
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  2. W. Leclerc
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Correspondence to H. Haddad.

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Funding

The authors would like to gratefully acknowledge the European Union for the financial support under the INTERREG IV France-Wallonie-Vlaanderen Program PRISTIFLEX (\(\hbox {N}^{\circ }\) FW 1.1.28), and the région de Picardie for funding the CASIMAT Program.

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Haddad, H., Leclerc, W., Guessasma, M. et al. Application of DEM to predict the elastic behavior of particulate composite materials. Granular Matter 17, 459–473 (2015). https://doi.org/10.1007/s10035-015-0574-0

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