脆性多裂纹扩展问题的近场动力学建模分析

针对脆性多裂纹扩展问题，基于近场动力学（PD）理论开展本构建模与数值方法研究.在常规微弹脆性本构模型基础上引入物质点对的转动，同时在本构力模型中增加能够反映物质点间长程力尺寸效应的核函数，提高计算精度、效率和结果的稳定性.构建能够以统一的模型和算法自然模拟脆性多裂纹扩展全过程的PD数值体系.通过定量分析确定最佳近场尺寸及核函数，通过双裂纹巴西圆盘和多裂纹脆性板的破坏过程模拟验证所提模型和算法，结果表明：改进型PD模型和数值方法可以定性、定量分析脆性多裂纹扩展问题.模拟单轴拉伸荷载作用下双裂纹脆性板的裂纹扩展过程，得到了初始裂纹分布情况对结构破坏形式和承载能力的影响规律.

Peridynamic modelling and simulation for multiple crack propagation in brittle materials

An improved peridynamic (PD) constitutive model and corresponding numerical method were proposed to analyze the multiple crack propagation in brittle materials. The rotation of the bond of material points was introduced into the conventional microelastic brittle PD model; a kernel function reflecting the internal length effect of long-range forces between material points was implemented into the constitutive force model, to improve the accuracy, efficiency and stability of calculation. Meanwhile, a numerical system under the framework of PD was developed to simulate the multiple crack propagation in brittle materials naturally with the uniform model and algorithms. The most effective peridynamic horizon size and kernel function were confirmed through quantitative analysis. The proposed model and algorithms were validated through the disruptive process simulation of a double-notched Brazilian disk and a brittle plate with multiple cracks. Results show that the improved PD model and numerical method can analyze the brittle crack propagation problem, qualitatively and quantitatively. Moreover, the crack propagation in a brittle plate with two pre-existing cracks under uniaxial tension was analyzed, then the influence rule of the initial cracks' distribution on the stucture's failure mode and failure load is discovered.