基于近场动力学方法的结构准静态变形的定量计算

近场动力学(Peridynamics,PD)是一种新兴的基于非局部模型描述材料特性的数值计算方法.该方法假定位于连续体内的粒子通过有限的距离与其他粒子相互作用,通过积分计算在一定近场范围(horizon)内具有一定影响域的材料点之间的相互作用力,而不论位移场的连续与否,避免了传统的局部微分方程求解在面临不连续问题时的奇异性和现有多尺度算法的复杂性.在近场动力学理论框架下,考虑近场范围尺寸对本构力函数的影响,构造了二次多项式型本构力核函数,对反映物质点长程力基本特性的本构力函数进行改进.通过引入人工阻尼、构建分级加载算法和系统失衡判断准则,使近场动力学方法能适用于定量的准静态变形的计算分析.

Quatitative calculation of quasi-static deformation of structurebased on peridynamics theory

Peridynamics (PD) is a continuum theory that employs a nonlocal model to describe material properties. The theory assumes that particles in a continuum interact with each other across a finite distance, and formulates problems in terms of integral equations rather than partial differential equations. In this paper, an improved material model for the elastic deformation and quasi-static fracture analysis of materials and structures were proposed within the framework of the PD. The model enables accurately analyzing quasi-static elastic behavior of materials and structures under external loads by implementing a local damping into the peridynamic equations of motion and employing a quasi-static step loading method. The qualitative and quantitative validity of the model was established through numerical examples.