A new thermomechanical fracture analysis approach for 3D integration technology
In this study, the peridynamic framework is applied to model heat diffusion to derive peridynamic heat diffusion equations. A numerical scheme is put forward and implemented in order to establish the validity of these equations. Finally, an approach is developed for coupled solution of heat conduction and solid mechanics equations in the realm of peridynamics.
Refined bond-based peridynamics for thermal diffusion
PurposeThis paper aims to review the existing bond-based peridynamic (PD) and state-based PD heat conduction models, and further propose a refined bond-based PD thermal conduction model by using the PD differential operator.Design/methodology/approachThe general refined bond-based PD is established by replacing the local spatial derivatives in the classical heat conduction equations with their corresponding nonlocal integral forms obtained by the PD differential operator. This modeling approach is representative of the state-based PD models, whereas the resulting governing equations appear as the bond-based PD models.FindingsThe refined model can be reduced to the existing bond-based PD heat conduction models by specifying particular influence functions. Also, the refined model does not require any calibration procedure unlike the bond-based PD. A systematic explicit dynamic solver is introduced to validate 1 D, 2 D and 3 D heat conduction in domains with and without a crack subjected to a combination of Dirichlet, Neumann and convection boundary conditions. All of the PD predictions are in excellent agreement with the classical solutions and demonstrate the nonlocal feature and advantage of PD in dealing with heat conduction in discontinuous domains.Originality/valueThe existing PD heat conduction models are reviewed. A refined bond-based PD thermal conduction model by using PD differential operator is proposed and 3 D thermal conduction in intact or cracked structures is simulated.
The Invariance of the Vacuum is the Invariance of the World
The following theorem is demonstrated: If the vacuum is invariant under the group generated by the space integral of the time component of a local vector current, then the Hamiltonian is invariant also. A similar theorem holds for the group generated by the space integral of a space component of a local axial-vector current.