Weave geometry generation avoiding interferences for mesoscale RVEs

An algorithm which allows the generation of representative volume elements (RVEs) for complex woven and warp-interlaced fiber-reinforced composite topologies while avoiding unphysical tow intersections is presented. This is achieved by extending an existing RVE generation strategy in two significant ways: (1) the local cross section shape of the tow is adjusted depending on the local tow curvature in a way that preserves the cross sectional area of the tow, and (2) the elementary crimp interval is separated into a planar and a transition region. The modifications facilitate the generation of a wide range of elaborate textile topologies without tow intersections, which are present without the proposed modifications unless complex tow to tow contact models are introduced. The mechanical properties of plain weaves were predicted based on the topology generated with the proposed algorithm as well as based on RVEs which were constructed based on actual micrographs, i.e. a “digital twin” of the actual microstructure. A comparison of the predicted mechanical properties based on finite element and Multiscale Generalized Method of Cells techniques shows close agreement. However, some differences exist with respect to experimentally determined material parameters due to the finite dimensions of the specimens. Lastly, mechanical properties of multilayered weaves are predicted with the finite element method. The considered material systems are carbon fiber in epoxy matrix as well as C/C-SiC. However, the procedure is applicable to a wide range of material systems.     

有限元法在砌体结构分析中的应用

目的 研究有限元法在空间砌体结构分析中应用的可行性。并提出模拟砌体带裂缝损伤状态的有限元建模及分析方法．方法 进行砌体结构模型拟静力试验及脉动测试．并采用等效体积单元法对空间砌体结构模型进行有限元分析．在对有限元模型的优化更新研究中，以损伤状态下的识别刚度作为目标函数。根据结构位移、抗侧移刚度及外荷载三者的内在关系，通过调整弹性模量优化有限元模型来模拟砌体带裂缝工作状态，并对比拟静力试验及动态测试识别结果进行理论分析．结果 利用所提出的有限元建模及分析方法很好地模拟了砌体结构完好及带裂缝损伤状态下的工作特性．有限元模型计算分析结果与实测值具有良好的一致性．结论 采用等效体积单元（RVE）可以准确模拟空间砌体结构的材料特性．利用动态测试数据结合反演理论进行结构模型的优化更新方法可有效模拟砌体结构的带裂缝工作状态，并有效地考虑砌体材料的离散性问题。     

Grain-level statistical plasticity analysis on strain cycle fatigue of a FCC metal

The micromechanical strain cycle fatigue-life is systematically investigated by the micro-level numerical simulation, compared with symmetrical strain cycle experiments of copper, focusing on the characteristics of polycrystalline aggregation and the mechanism of microscale plastic deformation. A methodology to predict the low-cycle fatigue life by micro-level simulation along with statistical analysis is proposed through the following steps: (1) A crystal plasticity model is developed based on the nonlinear kinematic hardening mechanism of crystal slipping system. This model is applied to the calculations of crystal grain interior stresses and plastic strains. (2) A statistical representative volume element (SRVE) is constructed for a pure copper as a material model which features a polycrystalline Voronoi aggregation consisting of a number of crystal grains. This SRVE can be used for statistical analysis of the material inhomogeneous stresses and strains during cycle loading. (3) The simulations are performed to model the experimental cycle evolution of strain fatigue by using the SRVE under the symmetrical tensile–compressive loading. (4) Statistical and micromechanical analyses are carried out for the inhomogeneous interior stresses and strains of the SRVE of the polycrystalline copper in the low cycle regime. The resulting analysis can render the microscale interpretation and numerical simulation for the low-cycle fatigue evolution accordingly.     

平纹织物复合材料横向力学性能研究

通过对平纹织物复合材料的横向拉压试验, 分析了产生各种破坏现象的微观机理。横向压缩过程中,在与水平面成45°方向剪切破坏的同时还出现层间裂纹。由于两个方向上纱线的弯曲程度不同, 破坏形式有很大差异, 不同自由边处的纱线界面存在不同程度的剪切破坏, 并表现出不同的边缘效应。借助显微镜观察和基于代表体积单元的数值模拟对这些现象进行了分析, 发现高度不均匀的内部波纹纱线结构在横向压缩下产生的层间剪切应力是出现横向裂纹的主要原因。      

基于均质化方法的钢丝网砂浆加固土坯墙体抗震性能研究

应用等效体积单元(Representative Volume Element简称RVE)方法对3片土坯墙体试件的低周反复加载试验进行数值计算分析,并与试验结果进行对比,验证了RVE方法应用于土坯墙体的合理性。在此基础上,对钢丝网水泥砂浆加固的土坯墙体采用二次RVE方法进行数值计算,分析土坯墙体加固前后的抗震性能,验证了钢丝网水泥砂浆加固土坯墙体的有效性与二次RVE方法应用于加固土坯墙体数值计算的可行性。研究成果可为村镇传统生土建筑的改造与抗震加固设计提供参考依据。     

平纹织物复合材料的弹性模量预测

利用细观力学的代表体积元(RVE)法,预测了平纹织物复合材料的弹性模量。建立了表征RVE形态的数学模型,分析了细观结构与宏观性能之间的关系,编制了从组分材料的弹性性能推测复合材料的弹性性能的预测程序。对理论预测进行了实验验证,理论值与实测值在一定误差范围内能较好吻合,说明此预测方法具有一定的可靠性。     

Two‐scale finite element modelling of reinforced concrete structures: Effective response and subscale fracture development

A two‐scale model is derived from a fully resolved model where the response of concrete, steel reinforcement, and bond between them are considered. The pertinent “effective” large‐scale problem is derived from selective homogenisation in terms of the equilibrium of reinforced concrete considered as a single‐phase solid. Variational formulations of the representative volume element problem are established in terms of the subscale displacement fields for the plain concrete continuum and the reinforcement bars. Dirichlet and Neumann boundary conditions (BCs) are imposed on the concrete (pertaining to uniform boundary displacement and constant boundary traction, respectively) and on the reinforcement bars (pertaining to prescribed boundary displacement and vanishing sectional forces, respectively). Different representative volume element sizes and combinations of BCs were used in FE² analyses of a deep beam subjected to four‐point bending. Results were compared with those of full resolution (single‐scale). The most reliable response was obtained for the case of Dirichlet‐Dirichlet BCs, with a good match between the models in terms of the deformed shape, force‐deflection relation, and average strain. Even though the maximum crack widths were underestimated, the Dirichlet‐Dirichlet combination provided an approximate upper bound on the structural stiffness.     

A novel reliability-based topology optimization framework for the concurrent design of solid and truss-like material structures with unknown-but-bounded uncertainties

A new nonprobabilistic reliability-based topology optimization method for continuum structures with displacement constraints is proposed in this paper, in which the optimal layout consists of solid material and truss-like microstructure material simultaneously. The unknown-but-bounded uncertainties that exist in material properties, external loads, and safety displacements are considered. By utilizing the representative volume element analysis, rules of macro-micro stiffness performance equivalence can be confirmed. A solid material and truss-like microstructure material structure integrated design interpolation model is firstly constructed, in which design domain elements can be conducted to select solid material or truss-like microstructure material by a combination of the finite element method in the topology optimization process. Moreover, a new nonprobabilistic reliability measuring index, namely, the optimization feature distance is defined by making use of the area-ratio ideas. Furthermore, the adjoint vector method is employed to obtain the sensitivity information between the reliability measure and design variables. By utilizing the method of moving asymptotes, the investigated optimization problem can be iteratively solved. The effectiveness of the developed methodology is eventually demonstrated by two examples.