有限变形下非均质材料的力学及热弹性随机均化分析
发布时间:2018-06-20 14:06
本文选题:随机均化 + 非均质材料 ; 参考:《西安电子科技大学》2015年硕士论文
【摘要】:二相非均质材料是基体和增强体(或夹杂)组合而成,它可以充分发挥其组分材料的优点,同时克服单一材料的缺陷。由于非均质材料具有高强度、低密度、易加工、可设计性强、耐侵蚀等各种优良特质,因而广泛地应用于现代国民生产生活的各个方面,非均质材料结构与力学性能的研究也日益成为热点研究课题。此外,材料在加工制造过程中不可避免地要受到各种随机因素的影响,因此在对非均质材料的等效力学性质进行分析研究时,非常有必要考虑其微观结构参数的随机性以及同一成分参数间的相关性。本文在有限变形条件下,对非均质材料进行了力学和热弹性的随机均化分析。首先介绍了非均质材料分类与应用、相关研究的背景和现状。然后给出了表征体积单元(RVE)的定义及生成方法。在此基础上,给出了力学和热弹性两种情况下的基于有限单元法(FEM)的均化方法,包括边界条件的介绍及微观与宏观尺度下材料等效特性的求解。在蒙特卡洛法的基础上,给出了力学和热弹性两种情况下的随机均化框架,对非均质材料整体宏观随机等效性质及其数字特征值进行了求解。最后给出了力学及热弹性下的随机均化分析算例。在算例中,考虑材料微观结构形态及各组分性质的随机性以及同一组分参数之间的相关性,首先使用随机序列添加法(RSA)生成非均质材料的三维表征体积单元,其内部的夹杂颗粒呈随机分布;进而采用数值收敛法确定了不同体积分数下表征体积单元的尺寸;将多尺度方法、有限单元法和蒙特卡洛法相结合,求解了非均质材料的随机等效性质,如力学分析中通过将不同类型的边界条件施加于表征体积单元得到了等效剪切张量、第一Piola-Kirchhoff应力、应变能等参数,而在热弹性分析中则将求解过程分解成力学求解和热学求解两个阶段,得到了应力张量、热流量张量、变形梯度张量等有效性质;最后通过数理统计方法求得了各等效量的数字特征值并考察了不同随机参数及其相关性对材料随机等效特性的影响程度。
[Abstract]:Two-phase heterogeneous materials are composed of matrix and reinforcements (or inclusions), which can give full play to the advantages of their component materials and overcome the defects of single materials. Due to its high strength, low density, easy processing, good designability, corrosion resistance and so on, heterogeneous materials are widely used in all aspects of modern national production and life. The research on the structure and mechanical properties of heterogeneous materials has become a hot topic. In addition, the material is inevitably affected by various random factors in the process of manufacturing. Therefore, in the analysis of the equivalent mechanical properties of heterogeneous materials, It is necessary to consider the randomness of the microstructure parameters and the correlation among the same component parameters. In this paper, the random homogenization analysis of mechanics and thermoelasticity of heterogeneous materials is carried out under the condition of finite deformation. Firstly, the classification and application of heterogeneous materials, the background and status of related research are introduced. Then, the definition and generation method of the representation volume unit RVEare given. On this basis, a homogenization method based on finite element method (FEMM) for both mechanical and thermoelastic cases is presented, including the introduction of boundary conditions and the solution of the equivalent properties of materials at micro and macro scales. On the basis of Monte Carlo method, the random homogenization frame under two conditions of mechanics and thermoelasticity is given, and the macroscopic stochastic equivalent properties of heterogeneous materials and their numerical eigenvalues are solved. Finally, an example of random homogenization analysis under mechanics and thermoelasticity is given. In the example, considering the randomness of the microstructure and properties of each component and the correlation between the parameters of the same component, the random sequence addition method (RSAs) is used to generate the three-dimensional representation volume unit of the heterogeneous material. The inclusion particles are randomly distributed in its interior, and then the size of the volumetric element is determined by numerical convergence method, and the multi-scale method, the finite element method and the Monte Carlo method are combined. The random equivalent properties of heterogeneous materials are solved. For example, the equivalent shear Zhang Liang, the first Piola-Kirchhoff stress, the strain energy and so on are obtained by applying different boundary conditions to the characterizing volume element in mechanical analysis. In thermoelastic analysis, the solution process is decomposed into two stages: mechanical solution and thermal solution. The effective properties of stress Zhang Liang, heat flow rate Zhang Liang and deformation gradient Zhang Liang are obtained. Finally, the numerical eigenvalues of the equivalent quantities are obtained by mathematical statistical method, and the influence of different random parameters and their correlation on the random equivalent properties of materials is investigated.
【学位授予单位】:西安电子科技大学
【学位级别】:硕士
【学位授予年份】:2015
【分类号】:TB301
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