近场动力学研究进展

A Review on Advances in Peridynamics

近场动力学(Peridynamics或PD)理论基于非局部作用思想,采用空间积分描述物质内部作用,对于从连续到非连续、微观到宏观的力学行为具有统一的表述,数值上天然具有无网格属性和不连续求解功能,在分析不连续,多尺度等问题时展现出了具有优势的适用性和可靠性.本文介绍了近场动力学的发展背景;概述了其理论基础、数值实现过程和计算体系,并在此基础上探讨了近场动力学理论和数值模型的适定性,以及与传统连续介质模型和分子动力学模型进行耦合的可行性;系统分析了近场动力学方法在各个领域上的应用发展现状和趋势,包括静态、动态破坏问题,基于近场动力学的材料模型,以及新兴的疲劳问题研究和多尺度、多物理场的耦合问题;最后对近场动力学方法目前存在的局限性和将来的研究进行了探讨.

Peridynamics （PD） is a nonlocal theory, and it employs integral operator to describe mechanical interactions inside materials and thus applies an uniform model to the mechanical behaviors from continuity to non-continuity and microscopic to macroscopic. Main numerical methods based on peridynamics naturally have meshfree properties and show advantageous applicability and reliability in analysis of discontinuous, multiscale problems. In this paper, the evolving research progress of peridynamics is reviewed. Its theoretical foundation, numerical implementation, and computing system are briefly summarized. The well-posedness of peridynamics numerical model as well as its feasibility of coupling with traditional continuum model or molecular dynamics model is then discussed. The development status and trend of peridynamics in various fields are presented systematically, including the static and dynamic failure problems, the material model in peridynamics framework, the fatigue problems and the coupling models of multiscale and multiphysics. Finally, current limitations and the needs for future research of peridynamics are discussed.