Summary The peridynamic theory reformulates the equations of continuum mechanics in terms of integro‐differential equations instead of partial differential equations. It is not straightforward to apply the available artificial boundary conditions for continua to peridynamic modeling. We therefore develop peridynamic transmitting boundary conditions (PTBCs) for 1D wave propagation. Differently from the previous method where the matching boundary condition is constructed for only one boundary material point, the PTBCs are established by considering the interaction and exchange of information between a group of boundary material points and another group of inner material points. The motion of the boundary material points is recursively constructed in terms of their locations and is determined through matching the peridynamic dispersion relation. The effectiveness of the PTBCs is examined by reflection analyses, numerical tests, and numerical convergent conditions. Furthermore, two‐way interfacial conditions are proposed. The PTBCs are then applied to simulations of wave propagation in a bar with a defect, a composite bar with interfaces, and a domain with a seismic source. All the analyses and applications demonstrate that the PTBCs can effectively remove undesired numerical reflections at artificial boundaries. The methodology may be applied to modeling of wave propagation by other nonlocal theories. Copyright © 2016 John Wiley & Sons, Ltd.
The development of advanced electronic devices is boosting many aspects of modern technology and industry. The ever‐increasing demand for advanced electrical devices and integrated circuits calls for the design of novel materials, with superior properties for the improvement of working performance. In this review, a detailed overview of the synthesis strategies of 2D metal organic frameworks (MOFs) acquiring growing attention is presented, as a basis for expansion of novel key materials in electrical devices and integrated circuits. A framework of controllable synthesis routes to be implanted in the synthesis strategies of 2D materials and MOFs is described. In short, the synthesis methods of 2D MOFs are summarized and discussed in depth followed by the illustrations of promising applications relating to various electrical devices and integrated circuits. It is concluded by outlining how 2D MOFs can be synthesized in a simpler, highly efficient, low‐cost, and more environmentally friendly way which can open up their applicable opportunities as key materials in advanced electrical devices and integrated circuits, enabling their use in broad aspects of the society.
The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and nonlocality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems. Some important issues attract much attention, such as the computation of infinite domains, the treatment of softening of boundaries due to an incomplete horizon, and time accumulation error in dynamic processes. In this work, we develop the boundary element method of peridynamics (PD-BEM). The numerical examples demonstrate that the PD-BEM exhibits several features. First, for nondestructive cases, the PD-BEM can be one to two orders of magnitude faster than the meshless particle method of peridynamics (PD-MPM) that directly discretizes the computational domains; second, it eliminates the time accumulation error, and thus conserves the total energy much better than the PD-MPM; third, it does not exhibit spurious boundary softening phenomena. For destructive cases where new boundaries emerge during the loading process, we propose a coupling scheme where the PD-MPM is applied to the cracked region and the PD-BEM is applied to the uncracked region such that the time of computation can be significantly reduced.
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