Numerical and analytical description of the mechanical properties of quasi tetrahedral agglomerates

• The configuration and coordinates of quasi tetrahedral agglomerates are derived.
• The force distribution of tetrahedral agglomerates at compression is derived.
• An approach for elastic contact deformation of the primary particles is derived.
• The approach gives a limiting curve for high bond stiffnesses.

Quasi tetrahedral agglomerates consist of four spherical primary particles, of which three primary particles generally form a mechanically stable base on which the fourth primary particle is arranged centrally (as in the regular case, where the primary particles have equal radii) forming an apparent trigonal pyramid.The coordinates of the centers of the primary particles are derived for agglomerates composed of monodisperse spherical primary particles (regular tetrahedron) and polydisperse spherical primary particles (skewed tetrahedron). Moreover, the force distribution within the agglomerates at compression is described and an analytical model for elastic contact deformation is derived on the basis of the Hertz model [1].Following, the regular structure of the agglomerates is experimentally analyzed using compression tests and the recorded force–displacement curves are evaluated with the new analytical model. Additionally, mechanical properties like the modulus of elasticity and the yield point of the primary particles as well that as of the tetrahedral agglomerates are also derived.Subsequently, tetrahedral agglomerates are modeled using the discrete element method (DEM) and their compression behavior between two rigid plates is simulated. The received numerical force–displacement curves are compared with the model-based approximated analytical force–displacement curves. Force–displacement curves of agglomerates composed of poly-disperse spherical primary particles are recorded and evaluated as well. It was found that the regular tetrahedron represents the most stable configuration, with an upper threshold force–displacement curve on varying the upper primary particle size and limiting curves on varying the size of one of the lower primary particles.

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