分级材料变形与失效的分级有限元分析

项目名称： 分级材料变形与失效的分级有限元分析

项目编号： No.11272245

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李录贤

作者单位： 西安交通大学

项目金额： 82万元

中文摘要： 由于在多个尺度上的分级结构，分级材料同时具有较好的强度和韧性以及缺陷容差能力强等诸多在微观或细观层次才能表现出的卓越特性。目前，分级材料在工程领域正在得到越来越广泛的应用，因而，其特殊的力学性能成为学术界重点研究的课题之一。本项目以骨类、木材及壁虎粘附垫三类具有代表性微观几何形貌的分级材料为研究对象，首先建立各类材料典型的几何和力学模型，对简单分级材料的简单变形和失效过程进行理论分析；然后运用混合（HR）变分原理，通过引入新概念形函数，发展分级有限元方法，编制分级有限元程序，对典型复杂分级材料的变形和失效进行高效高精度分析，揭示分级材料微观或细观层次优良性能延伸至宏观层次的机理，为天然分级材料的应用提供基础理论和数值分析手段；最后运用分级有限元法，数值分析和比较不同结构分级材料的力学行为，提出不同承载条件下分级材料的最优分级结构，为人工分级材料的设计提供参考。

中文关键词： 分级自相似材料；缺陷不敏感性；本构关系；特征参数；高阶梁板理论

英文摘要： Due to hierachical structures in more than one length scales, hierachical materials exhibit many extraordinary properties such as superior strength and toughness and flaw insensibility which exist only in micro or meso scales. Recently, hierachical materials attain more and more prevailing applications in engineering, and therefore their mechanical behaviours attract much attention of researchers. Aiming at three kinds of hierachical materials, i.e. bone, wood and attachment pads of gecko, which have quite different micro-geometric profiles, the typical geometric and mechanical models are firstly built, and the deformation and failure analyses are then theoretically carried out for simple problems with simpler geometric and mechanical models. Next, applying the mixed (HR) variational principle, the hierachical finite element method (HFEM) is proposed by introducing the new concept shape functions, and then corresponding computer code is developed. With the HFEM, the deformation and failure analyses are numerically conducted for complex hierachical materials in order to better understand the mechanism that the superior properties in micro or meso scales still retain in the macro length scale, which will supply the fundamentals and the numerical means for utility of natural hierachical materials. Finally, the mech

英文关键词： Hierarchical self-similar materials；Flaw tolerance；Constitutive relation；Characteristic parameter；Higher-order theory of beam and plate