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Modelling heat conduction is of significant importance for evaluating temperature effects of granular materials. Since the randomness of the grain structure and the heat resistance characteristics of grain interfaces, to realistically modelling the heat conduction of granular materials, the heat interactive among these random-shaped grains should be correctly reflected. In this study, the numerical manifold method (NMM) is extended to model the transient heat conduction of granular materials. The random-shaped grain structure of granular materials is represented with Voronoi polygons. The heat interactive among grains is realistically simulated by inserting heat conductive cohesive elements between grain boundaries. Besides, an interfacial heat conductivity is defined for the cohesive element to better represent the heat conduct capacity of grain interfaces. As a result, the temperature jumps at grain interfaces are naturally captured due to the dual cover systems of the NMM, while the heat fluxes across the interfaces are assumed to be continuous. To validate the developed numerical method, a benchmark test is carried out. At last, effects of the grain characteristics and interfacial heat resistance on the temperature field as well as the effective heat conductivity (EHC) of a plane consists of granular material are investigated by the developed NMM. [ABSTRACT FROM AUTHOR]

In order to gain an insight into creep induced cracking in viscoelastic materials, the creep crack phenomenon in viscoelastic materials are numerically investigated in this paper based on the numerical manifold method (NMM). To more realistically capture the mechanical behaviour in the vicinity of crack tips, the local displacements around crack tips are enriched with the viscoelastic crack-tip asymptotic displacement field. To better represent the viscoelastic materials, an incremental viscoelastic constitutive law based on the generalized Kelvin-Voigt model is incorporated into the NMM. To achieve these treatments in the NMM, an incremental viscoelastic NMM formulation is derived. In addition, an incremental formulation of the mixed mode viscoelastic energy release rate (ERR), which can be tackled in the same process with the incremental viscoelastic constitutive law, is derived and incorporated into the NMM for investigating the variations of the ERR in viscoelastic materials. Based on the developed method, three creep crack problems with different loading conditions and pre-existing crack configurations are simulated, and the crack opening and sliding displacements as well as corresponding mixed mode ERR are analysed. Simulation results show good agreement with the theoretical solutions, which indicate that the proposed NMM is suitable for complex creep crack problems. [ABSTRACT FROM AUTHOR]

In the classical numerical manifold method (NMM), contact conditions are enforced by applying or releasing contact springs repeatedly. Penalty spring stiffness is constant during the calculation process. In this study, a modified contact model describing joint mechanical behavior is proposed using the NMM. Two rock joint constitutive models, namely the BB model and hyperbolic model, are used to modify normal and shear stiffness, respectively. In the modified contact model, stiffness varies with normal and shear inter-penetration distance in each iteration step. Therefore, stiffness varies for different contact points. With increasing inter-penetration distance, the normal stiffness increases and shear stiffness decreases. As a result, the force needed for trigger sliding along the joint increased. Finally, three example simulations are conducted to validate the effectiveness of the modified contact model. [ABSTRACT FROM AUTHOR]