Discrete Element Method for the thermal field: Proof of concept and determination of the material parameters

The physical behaviour of materials and complicated components is nowadays numerically predicted by using the Finite Element Method (FEM). Another method, older than the finite element idea, is the Discrete Element Method (DEM), with which it is possible to make continuum-based calculations not only in the mechanical field but also in the thermal field, as will be shown in this paper.One major drawback of the FEM is that continuum-based methods are unable to include the stochastically distributed microscopic effects in the macroscopically oriented calculations. The Discrete Element Method is one method with which these effects can be considered.For making realistic fracture and life time predictions for components at high temperatures, it is important to adapt the DEM for the thermal field. This paper describes the mathematical proof of the 2D Discrete Element Method (or Lattice Model) for the thermal field. It will specifically be shown that the heat flux inside the framework can be transferred to the heat conduction equation. Furthermore, some examples demonstrate how the heat flux can be calculated with this method and how the corresponding material parameters are found and implemented. Also, as will be shown in this paper, anisotropic or orthotropic heat flux effects can be integrated in the DEM model.

► The Discrete Element Method for the thermal field is introduced.
► A mathematical proof for rectangular and hexagonal elements is provided.
► It is shown that hexagonal Discrete Elements can determine 2D temperature fields.