标题： 代表性体积单元：裂纹非均质介质中的存在与范围 显示英文标题

标题： Representative Volume Element: Existence and Extent in Cracked Heterogeneous Medium

摘要： 鉴于工程行业中对复合材料日益增长的需求，本文专注于微观尺度上复合材料的失效，并增强多尺度建模技术的使用，以使其适用于各种应用。 本研究旨在通过减弱代表性体积单元（RVE）建模中的网格和尺寸敏感性，提高体积单元的代表性。 提出了一种减轻RVE建模中网格敏感性的技术，该技术使计算分析中观察到的断裂能与实际现象相等，从而保持响应独立于应变局部化带宽。 基于确保应变周期性（除了在域边界处的位移周期性）以及补充周期性边界条件（PBCs）的能力以减弱RVE建模中的尺寸依赖性的假设，制定了一组修改后的周期性边界条件（MPBCs）。 对一千二百个落入五种纤维体积分数和四种RVE尺寸组合的RVE样本进行横向加载分析，验证了MPBCs在减弱RVE尺寸对材料响应精度的影响方面的能力，特别是在非弹性区域。 本研究还关注影响二维复合材料RVE中损伤起始的各种因素。 观察到一对纤维的排列方式，其成员彼此靠近，使得加载方向与它们中心之间绘制的假想线之间的角度较小，这种排列方式使得它们之间的区域更易于产生损伤。 显示英文摘要

摘要： Acknowledging the ever-increasing demand for composites in the engineering industry, this paper focuses on the failure of composites at the microscale and augmenting the use of multiscale modelling techniques to make them better for various applications. This work aims to increase the representativeness of the volume element by attenuating the mesh and size sensitivities in representative volume element (RVE) modelling. A technique to alleviate mesh sensitivity in RVE modelling is proposed, which equalises the fracture energy observed from computational analysis with the real phenomenon, thereby keeping the response independent of the bandwidth of strain localisation. Based on the hypothesis that ensuring periodicity of strain, in addition to displacement periodicity across the domain boundary and supplementing the capability of periodic boundary conditions (PBCs) to attenuate the size dependency in RVE modelling, a set of modified PBCs (MPBCs) are formulated. One thousand two hundred RVE samples falling into combinations of five fibre volume fractions and four RVE sizes are analysed under transverse loading, and the ability of MPBCs to attenuate the effect of RVE size on the precision of material response, particularly in the inelastic regime, is verified. This work also focuses on various factors affecting damage initiation in 2D composite RVEs. The arrangement of a pair of fibres with their members placed close to each other, such that the angle between the direction of loading and an imaginary line drawn between their centres is less, is observed to make the region between them more favourable to damage.