高精度近场动力学方法:一维键型研究

近些年发展起来的近场动力学方法对于模拟复杂的断裂破坏问题具有显著优势.然而,计算精度不高一直是影响该方法进一步发展的瓶颈问题之一.区域积分不精确和键缺失导致的边界效应是降低该方法计算精度的两个主要原因.针对一维键型近场动力学模型,本文通过修正微模量提高区域积分的精度,通过理性构建固定边界和力边界虚拟键改善边界效应,建立了高精度近场动力学方法.数值结果表明,与经典的近场动力学方法相比,本文方法显著提高了计算精度,准静态常应变问题甚至能够达到机器精度.

High-precision peridynamics: one dimensional bond-based model

Peridynamics (PD) developed in recent years possesses remarkable superiorities in modelling complicated fracture problems.However,its computational accuracy is unsatisfactory.This is one of the bottleneck issues which limit the further development of this theory.The inaccurate domain integration and surface effect induced by the lack of bonds are the two main reasons which lead to low accuracy.Aiming at one-dimensional bond-based PD model,this paper presents a high-precision PD (hp-PD) method in which the accuracy of domain integration is improved by correcting the micro-modulus and the surface effect is improved by rationally establishing the virtual boundary bonds of fixed and traction boundaries.Numerical results show that,in comparison with the traditional PD method,the proposed method remarkably improves the computational accuracy and for quasi-static constant strain problems the accuracy even reaches the machine precision.