Simulation of continuum electrical conduction and Joule heating using DEM domains

Abstract

This paper proposes an original method to simulate the electrical conduction in continuums with the Discrete Element Method (DEM). The proposed method is based on the graphs theory applied to electrical resistance network, where the resistance between two discrete elements is estimated through the notion of ‘transmission surface’ to assume the discrete domain as a continuous medium. In addition to the electrical conduction, the Joule heating of a DEM domain has also been developed to take full advantage of the electrical conduction. The proposed method has been implemented in the free DEM software named ‘GranOO’. The numerical results were compared against analytical approaches when applicable, or against Finite Element Method if the geometries become more complex or in case of dynamic loadings. The results are found satisfactory with errors around 3% for the electrical conduction and Joule heating of reasonably complex domains and loading cases. When it comes to more complex domains, such as electrical constriction, whilst the results remain close to those obtained with reference solutions (around 6%), they highlight the importance of taking care about the domains discretization. Finally, the proposed method is applied to detect cracks onset on a cylindrical rod torsion test to show how to take advantage of the proposed work.