近场动力学方法及其应用

近场动力学(peridynamics,PD)是一种新兴的基于非局部作用思想建立模型并通过求解空间积分方程描述物质力学行为的方法.它兼有分子动力学方法和无网格方法的优点,避免了基于连续性假设建模和求解空间微分方程的传统宏观方法在面临不连续问题时的奇异性,又突破了经典分子动力学方法在计算尺度上的局限,在宏/微观不连续力学问题分析中均表现出很高的求解精度和效率.首先概述了PD方法的理论基础、建模思路和计算体系;进而介绍了PD方法在不同尺度不连续力学问题中的应用,包括均匀与非均匀材料和结构的大变形、损伤、断裂、冲击、穿透和失稳问题,结晶相变动力学问题以及纳米材料和结构的破坏问题;最后讨论了PD方法在理论、计算和应用等方面值得进一步研究的问题.

A REVIEW ON PERIDYNAMICS(PD)METHOD AND ITS APPLICATIONS

Peridynamics (PD) is arecently developed theory in solid mechanics that employs anonlocal model of force interaction, and replaces the partialdifferential equations, such as the stress-strain relationship ofthe classical continuum theory, by an integral operator that sumsup internal forces separated by finite distances. It allowsdiscontinuities of various types to be modeled without applicationof special techniques to the discontinuous field and shows apromising prospect for solving practical problems in whichdiscontinuities form and grow spontaneously. Peridynamics has beensuccessfully applied to damage and failure problems at both macro-and micro-scales with satisfactory solution precision andnumerical efficiency. Without pathological defects of traditionalmethods when facing discontinuous problems, and excluding thecomputational limitations in length and time scales, peridynamicsshows great potential analogous but advantageous to both classicalmeshfree and molecular dynamic methods. The present paper firstreviews its theoretical basis, numerical scheme and modelingmethod, and then elucidates its application to discontinuousproblems at different scale, including damage, fracture, impact,penetration and stability analysis for macro-scale homogeneous andheterogeneous materials and structures, kinetics analysis forphase transformations and atomistic analysis for nanoscalematerials. Finally, some unsolved problems and future researchtrends in PD are discussed.