Simulation of heat conduction and thermal cracking of brittle materials using the particle-based discontinuous deformation analysis

This paper proposes a particle heat conduction and expansion model (PHCE) in the context of particle-based discontinuous deformation analysis (PDDA) to simulate the heat conduction and thermal cracking of brittle materials. The thermal-mechanical coupling model consists of three parts. In the first part, a virtual rectangular heat conduction channel is assumed between each active contact pairs. The temperature distribution is solved based on the heat conduction equation and the network of the channels. In the second part, the particle radii are updated according to the thermal expansion. In the third part, the mechanical analysis is carried out with the new particle radii. To correctly reproduce the macroscopic thermal conductivity, a geometrical correction factor is introduced, which is found related to the porosity and coordination number. The proposed coupling model, abbreviated as PHCE-PDDA, is verified by three examples, the steady-state heat conduction, transient heat conduction and the thermal mechanical coupling test. Furthermore, two thermal cracking problems are also modeled. The initiation and propagation of the thermal cracks can be well captured. The final crack patterns agree well with those observed from experiments, indicating that the proposed method is effective for the modelling of heat conduction and thermal cracking in brittle materials.