准静态变形破坏的近场动力学分析

摘要

基于近场动力学理论，提出新的更能反映非局部长程力特性的物质点间作用力函数，并通过在物质点运动方程中引入局部阻尼、构造分级加载算法和系统失衡判断准则，实现了采用统一的近场动力学模型和算法进行从准静态变形、裂纹萌生和扩展直至结构破坏全过程的连续模拟和准确定量计算。%An improved bond-based material model for the elastic deformation and quasi-static fracture analysis of materials and structures has been proposed within the framework of the peridynamic (PD) theory.This 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 effects of the magnitude of the local damping on the accuracy and efficiency of elastic calculation has also been investigated.Meanwhile,the complex failure phenomena such as spontaneous crack propagation can be predicted as a capability inherited from the peridynamic theory.Thus the whole mechanical response of materials and structures,from elastic deformation to crack initiation and propagation until ultimate breaking,can be analyzed with the identical model.In the proposed model,another important feature lies in the micromodulus of the pair-wise bond, which is described as a continuous function of the distance between two particles within the material horizon,and which is demonstrated to be more accurate compared to the previous PD models using a fixed stiffness constant to describe the interaction of particles.The qualitative and quantitative validities of the model have been established through numerical examples.