多孔复合材料一般不完美界面理论建模及数值计算
发布时间：2024-01-30 12:35
复合材料具有优异的力学性能,而且能根据实际需要设计和制造,被广泛应用于航空航天、国防事业、土木工程、医学仿生等各个领域。复合材料是由基质相、增强相和过渡层组成的多相材料。在生产过程中,由于复杂的工艺,在基质相和增强相之间会形成一层微观结构和物理特性明显不同于基质相和增强相的过渡层。过渡层的主要功能是传递载荷,对复合材料的力学性能有着显著的影响。因此研究过渡层的性质能够更清楚的了解复合材料的性能影响因素,进而建立复合材料的宏观性能同其组份材料性能及微观结构之间的关系,揭示复合材料在一定工况下的响应规律及其本质,为复合材料的优化设计、性能评价提供必要的理论依据和手段。过渡层的微观结构复杂,厚度小而且不容易精确测量,如果将过渡层作为有厚度的中间相相来处理,增加了理论分析和数值计算工作量甚至可能难以实现。针对饱和多孔复合材料,本论文建立了一种零厚度一般不完美界面模型等效替代过渡层。本论文的第一部分的主要内容是:以饱和多孔线弹性复合材料为研究对象,介绍了该材料在恒温条件下的本构关系。引入Hadamard’s关系和正交投影张量算子。在此基础上,借鉴Gu和He使用的方法,在几何上用零厚度的界面来替代...
【文章页数】：74 页
【学位级别】：硕士
【文章目录】：
摘要
Abstract
Chapter 1 Introduction
1.1 The background and significance
1.2 Process of the interface research
1.3 The development of the extended finite element
1.4 The works of this thesis
Chapter 2 Theoretical modeling of the general imperfect interface
2.1 The basic control equations
2.2 Surface differential operator
2.3 Hadamard’s relation
2.4 The general constitutive relation
2.5 Interfacial operators
2.6 The relations for perfect interfaces and imperfect interfaces
2.7 Jumps across the imperfect interface in the two-phase configuration
2.8 The four kinds of extreme cases
2.8.1 case 1
2.8.2 case 2
2.8.3 case 3
2.8.4 case 4
2.9 Summary
Chapter 3 Discretization of general imperfect interface
3.1 The simplified discontinuity of the generally imperfect interface
3.2 The strong and weak formulations for the boundary value problem of a partic-ulate composite
3.3 XFEM discretization
3.3.1 The level set function and enriched shape functions
3.3.2 The result of discretization
3.4 Summary
Chapter 4 Numerical implementation
4.1 The shape function and strain matrix of tetrahedron
4.2 The element types
4.3 Numerical integration
4.4 Summary
Chapter 5 Analytical solution and numerical solution to the boundary value problems involving a spherical general imperfect interface
5.1 Analytical solution to the boundary value problems
5.2 The extreme cases the analytical solution
5.2.1 case 1
5.2.2 case 2
5.3 Numerical result analysis
5.4 Summary
Conclusion
致谢
Bibliography
攻读硕士学位期间发表的论文及科研成果
本文编号：3890163
【文章页数】：74 页
【学位级别】：硕士
【文章目录】：
摘要
Abstract
Chapter 1 Introduction
1.1 The background and significance
1.2 Process of the interface research
1.3 The development of the extended finite element
1.4 The works of this thesis
Chapter 2 Theoretical modeling of the general imperfect interface
2.1 The basic control equations
2.2 Surface differential operator
2.3 Hadamard’s relation
2.4 The general constitutive relation
2.5 Interfacial operators
2.6 The relations for perfect interfaces and imperfect interfaces
2.7 Jumps across the imperfect interface in the two-phase configuration
2.8 The four kinds of extreme cases
2.8.1 case 1
2.8.2 case 2
2.8.3 case 3
2.8.4 case 4
2.9 Summary
Chapter 3 Discretization of general imperfect interface
3.1 The simplified discontinuity of the generally imperfect interface
3.2 The strong and weak formulations for the boundary value problem of a partic-ulate composite
3.3 XFEM discretization
3.3.1 The level set function and enriched shape functions
3.3.2 The result of discretization
3.4 Summary
Chapter 4 Numerical implementation
4.1 The shape function and strain matrix of tetrahedron
4.2 The element types
4.3 Numerical integration
4.4 Summary
Chapter 5 Analytical solution and numerical solution to the boundary value problems involving a spherical general imperfect interface
5.1 Analytical solution to the boundary value problems
5.2 The extreme cases the analytical solution
5.2.1 case 1
5.2.2 case 2
5.3 Numerical result analysis
5.4 Summary
Conclusion
致谢
Bibliography
攻读硕士学位期间发表的论文及科研成果
本文编号：3890163
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