Homogenization of Linear Elastic Properties of Silicon Nitride

The effective linear elastic properties of silicon nitride (Si₃N₄) are estimated based on first–, third–, and fifth–order bounds of the strain energy density. This specific type of material is a mixture of two linear elastic materials with different material symmetries. The β-Si₃N₄ grains have a hexagonal symmetry with significant amount of anisotropy, whereas the glassy phase is approximately isotropic. The results are as follows: i) The fifth–order upper and lower bounds are almost identical. Therefore, these bounds are sufficient for estimating the effective elastic properties. ii) For fixed elastic constants of the hexagonal β-Si₃N₄ grains, the effective properties of Si₃N₄ are determined as a function of properties of the glassy phase and its volume fraction. The corresponding diagrams allow for the inverse identification of the elastic properties of the glassy phase. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Simulation of Short Fibre Reinforced Composites

In this paper we present a way how short fibre reinforced composites, produced by injection moulding, can be simulated in a linear thermoelastic setting, with an instationary heat equation. The main problem is the unknown stochastic fibre orientation. The only information known about this orientation field are the first moments of its distribution. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Simulation of Short Fibre Reinforced Composites

Lightweight structures become more and more important and one great class within these structures are parts produced by injection moulding. To improve the mechanical properties of these parts short fibers are injected within the molten plastics. Now a way to describe these properties without knowing the fibre orientation exactly is needed. We show an intuitive way, how mechanical properties of short fibre reinforced composites for linear thermoelasticity can be described and show the relation to other approaches. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Simulation of Short Fibre Reinforced Composites

In this paper we present a way how short fibre reinforced composites, produced by injection moulding, can be simulated in a linear thermoelastic setting, with an stationary heat equation. The main problem is the unknown stochastic fibre orientation. The only information known about this orientation field are the first moments of its distribution. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic Deformation of Dispersely Failing Unidirectionally Reinforced Composites

A phenomenological model is proposed for describing the elastic deformation of a unidirectionally reinforced composite capable of accumulating scattered microdamages during its loading. The composite is considered as a homogeneous transversely isotropic solid. Its damaged state at every point is characterized by a centrally symmetric scalar function on the unit sphere (the damage function), which is used to account for variations in the elastic properties of the material during its deformation. The damage itself depends on the history of some equivalent strain, for which four simplified variants are suggested. The relation between strains and stresses is defined in a differential form. Dependences are presented for determining all unknown constants from simple mechanical experiments. As an example, an actual unidirectionally reinforced GFRP is considered, for which the main two-dimensional sections of corresponding failure surfaces are also constructed.     

Lamination Design Optimization for Continuous Fiber Reinforced Composites of Variable Thicknesses北大核心CSCD

由于具备高的比强度、比刚度,利用连续纤维增强复合材料代替传统金属材料以实现结构轻量化正受到设计者们的广泛关注。然而,结构的复杂性给复合材料的铺层设计与优化带来了很大的挑战。针对航空用复合材料铺层设计约束多的问题,通过逐步构建设计变量准确表达结构的铺层信息。基于经典遗传算法框架,结合各设计变量特点,定义了铺层优化算法中的遗传算子,通过引入“修复”策略保证了每一代解都能满足设计约束,分布在可行域区间内。最后利用精英保留策略提高了算法的局部寻优能力,可以降低复杂复合材料结构铺层设计的计算成本。通过解决经典benchmark问题并与已有优化结果的比较,验证了前述铺层优化算法的全局、局部寻优能力,为工程实际中的复合材料铺层设计优化提供了理论支撑。     

Incremental Scheme to Homogenize Anisotropic Elastic Properties of Multi-Phase Composites

An incremental homogenization scheme for the prediction of elastic properties of composites is reviewed. Similar to the differential scheme, the inclusions are included step-by-step. This approach accounts for high volume fractions of inclusion of different shape and elastic properties. A numerical example for a composite consisting of a polymeric matrix, glass fibers and voids is shown. The fiber distribution is chosen equivalently to a distribution in an injection molded short-fiber reinforced composite. The volume fraction of the voids is varied. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

纤维增强复合材料矩形薄板压缩稳定试验及最优设计

本文通过283块玻璃钢矩形薄板的稳定试验,得出试验结果与理论分析一致的结论,证实按各向异性板的屈曲理论公式计算纤维增强复合材料薄板稳定临界载荷是可靠的.本文也给出了各种纤维增强复合材料薄板达到最大临界载荷的最优基体含量和最优偏角的选择,得出的结果可供产品设计时使用.     

基于杂交应力元法的颗粒增强复合材料Monte-Carlo模拟

杂交应力元假设的高阶应力场可以用较疏的网格获得较高的计算精度.采用四叉树网格离散非均质计算域,四叉树杂交应力单元悬挂节点的位移协调条件自动满足,且得益于单元类型数量有限,单元刚度矩阵可以预计算,以便在实际计算时直接读取调用,大幅提高了计算效率.考虑夹杂的随机性对颗粒增强复合材料力学性能的影响,采用均匀化方法和Monte-Carlo方法,研究了随机夹杂的体积比、数量、长宽比对材料均质等效模量的影响,结果表明,复合材料的等效弹性模量随夹杂体积比、数量、长宽比的增大而增大,且对体积比最敏感.     

Analysis of Elastomeric Composites Based on Fiber Systems. 4. 3D Composites

The elastic properties of 3D elastomeric composite materials under large deformations are considered. The investigation is based on the structural macroscopic theory of stiff and soft composites. The results of micro- and macromechanical analyses of composite materials with compressible and poorly compressible matrices are presented. The character of interaction between the fibers of various reinforcing systems in these matrices is revealed. The deformation characteristics of the composites in tension and shear are presented as functions of their orientation and loading parameters. The evolution of the configuration of a composite material with a compressible matrix during loading is traced.     

Homogenization in the Modelling of Volume-Controlled Elastic Structures

The background for this article is the question of modification of the geometric configuration of an elastic structure by means of "volume"-type actuation. In this actuation mode stresses are applied to the elastic body by injection/extraction of a fluid into, or from, a large number of vacuoles in the elastic "matrix" material. Previous articles by the author, and others, have examined this process and studied its effectiveness in the context of a "naive" continuous model. The present paper develops modified models in the two-dimensional case by applying the "multiple scales" homogenization method to elastic bodies with increasingly small and numerous vacuoles arranged in a rectangularly periodic structure. The process leads to a modification of the naive model potentially useful in future elastic system control research.     

Homogenization of Fatigue and Creep Durability of Composites

The paper is an extension of the theory presented in [4] to fatigue, creep and other types of time‐dependent material behaviour. In the previous paper a multi‐phase periodic composite subjected to prescribed mechanical loads was considered. The asymptotic homogenization was applied for calculation of homogenized macro‐stresses. A nonlocal approximate macro‐strength condition, defined on homogenised stress‐field, was derived from the micro‐strength conditions and their convergence to the approximate macro‐strength condition, as the structure period tends to zero, was proved. This paper presents the analogous results for the macro‐durability of elastic and viscoelastic composites.     

Acoustic Band Structures and Homogenization of Periodic Elastic Media

Dispersion curves and frequency dependent velocity surfaces of periodic heterogeneous elastic media are determined from unit-cell problems using quasi periodic boundary conditions. Effective material parameters are obtained using a least square optimization of the phase velocities in the heterogeneous and the effective, generally anisotropic, homogeneous medium. For efficiency, a preconditioned iterative eigenvalue solver and a model order reduction scheme are used. This “dynamic” homogenization procedure is validated for frequencies below the first stop band employing FEM calculations on a finite structure consisting of an array of unit-cells and the effective homogeneous material. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization Approach Based on Laminates

In this work, a homogenization approach for the modeling of the material behavior of two-phase composites motivated by modeling a thin-layer-type microstructure is presented. The basic idea here is to idealize the thin-layered microstructure as a first-order laminate. In particular, a jump in deformation state across the phase interface is modeled constitutively via a rank-one connection of habit-plane type. In the material framework, the value for the jump as well as its direction remain as independent constitutive variables. However, in the case of laminates and an ideal plain interface, the direction is given and stays in a first approach constant. We assume that their values are determined by mechanical and configurational equilibrium in the two-phase composite at the interface. This yields to a set of implicit equations which lead to the corresponding response of the structure. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)