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Abstract:
In the present paper, a possibility of an approximation of elastic particulate composite with a network of elastic springs that undertake only axial forces is considered. It is assumed that the springs are equivalent to two hemispheres interacting through a weaker interface member. In a frame of the suggested approach, the description of the composite is limited to translational degrees of freedom, therefore, only a normal interaction between the spheres was considered. The methodology for calculation of the axial stiffness of the elastic springs and obtained solutions of the stiffness in explicit form are the main novelty of the article. A comparison of the stiffnesses of the springs obtained by the proposed methodology and by the three dimensional Finite Element Method (FEM) has shown a good agreement between them in a wide range of the ratio of the modulus of elasticity of the particles and matrix at four different distances between surfaces of the particles. A possibility of the approximation of particulate composite by springs was tested and discussed in details by comparing results of a mechanical response of a sample (under three different loading cases) modelled as a three dimensional solid and as a system comprised of the springs. The solutions were obtained by the FEM.

Keywords:
Spring network model, Lattice model, Particulate composites, Heterogeneous materials, Finite element modelling

Abstract:
The paper addresses discrete element (DEM) models of the heterogeneous particulate solids where the normal interaction between two deformable spherical particles bonded via weaker solid interface is considered. The integral interaction model aimed for evaluation of the bond stiffness was developed, where analytical expressions of the stiffness parameters reflecting individual contribution of the two particles and of the interface properties are derived. Application of the developed DEM model to particulate solid with many particles is considered. The accuracy and the suitability of this approach are evaluated by considering refined 3D Finite Element analysis.

Keywords:
Heterogeneous Solid, Particles Interaction, DEM, FEM