多物理场耦合作用分析的近场动力学理论与方法

广义来说, 近场动力学(peri-dynamics,PD)是假设每个物质点在承受一定范围内的非接触相互作用下,研究整个物理系统演化过程的理论,为涉及非连续和非局部相互作用的问题提供了一个统一的数学框架,具有广泛的适用性.在简要介绍诸多工程对于多物理场模型和数值计算软件的迫切需求后,针对现有商用软件在处理结构非连续演化问题时遇到的瓶颈,引入近场动力学理论和方法. 概述近场动力学固体力学模型,系统阐述近场动力学扩散模型和近场动力学多物理场耦合建模的研究现状和进展,主要涉及电子元器件、电子封装和岩土工程领域的多物理场耦合建模,包括热--力、湿--热--力、热--氧、热--力--氧、力--电、热--电、力--热--电、多孔介质的水--力流固相互作用等非耦合、半耦合与完全耦合模型,强调发展耦合方程数值解法的重要性.最后对扩散问题和多物理场耦合问题的近场动力学理论模型、数值算法和工程应用做进一步展望. 

Review of peridynamics for multi-physics coupling modeling

Generally, peridynamics is a theory focusing on the evolution of a physical system, which is based on the assumption that each material point interacts with the other material points within a certain domain through non-contact or nonlocal interactions. It provides a unified mathematical framework for analyzing problems involving the evolving discontinuities and nonlocality. After a brief introduction of the peridynamic solid models and the urgent requirements on multi-physics models and corresponding commercial software, which have the capability of dealing with the evolving discontinuities, we made a systematic review on peridynamic nonlocal diffusion and peridynamic multi-physics coupled modeling. It can be found that the existing multi-physics coupled modeling studies mostly concentrated on the problems in the electronic components, electronic packaging and geotechnical engineering fields, including the un-coupled, partial coupled and fully coupled models about thermo-mechanics, hygro-thermo-mechanics, thermo-oxidative, thermo-mechanics-oxidative, mechanics-electronics, thermo-electronics, thermo-mechanics-electronics, fluid-solid interaction model for porous medium. Finally, several potential problems in the theoretical model, numerical algorithm and engineering application of peridynamic diffusion modeling and multi-physics coupled modeling are suggested.