A method for the generation of 3D representative models of granular based materials

The morphology of many naturally occurring and man‐made materials at different length scales can be modelled using the packing of correspondingly shaped and sized particles. The mechanical behaviour of this vast category of materials – which includes granular media, particle reinforced materials and foams ‐ depends strongly upon the shape and size distribution of the particles. This paper presents a method for the generation and packing of arbitrarily shaped polyhedral particles. The algorithm for the generation of the particles is based on the Voronoi tessellation technique, whilst the packing is performed using a geometrical approach, which guarantees the non‐overlapping of the bodies without relying upon any, otherwise typically computationally expensive, contact detection and interaction algorithm. The introduction of three geometrical parameters allows to control the shape, size and spacial density of the polyhedral particles, which are used to build numerical models representative of densely packed granular assemblies, granular reinforced materials and closed‐cell foams. Copyright © 2017 John Wiley & Sons, Ltd.     

Modeling loading rate effect on crushing stress of metallic cellular materials

A mesoscale numerical model based on Voronoi tessellation is developed to investigate the loading rate effect on the crushing stress of cellular materials. The crushing stresses at both the impact and stationary ends of the Voronoi structures are simulated. The influences of the impact velocity, specimen size, inertia, and rate dependence of the base material on the crushing stress are discussed. The underlining reason for the argument on the rate dependence of cellular materials is clarified by comparing the current simulation results with the numerical results based on a continuum model and a shock wave theory. The conflicting observations from previous experimental studies on the dynamic behavior of cellular materials by different researchers are explained by the simulation results as well as the shock wave theory.     

A lumped mass numerical model for cellular materials deformed by impact

When impacted by a relatively rigid body, cellular materials undergo severe deformation and extensive material failure. However, such behaviour may not be well described using traditional numerical approaches such as the finite element method. This paper presents a lumped mass numerical model which can accommodate high degrees of deformation and material failure. The essence of this model is to discretize a block of material into contiguous element volumes, each represented by a mass point. Interactions between a node and its neighbours are accounted for by defining ‘connections’ that represent their interfaces which transmit stresses. Strains at a node are calculated from the co‐ordinates of the surrounding nodes; these also determine the stresses on the interfaces. The governing equations for the entire solution domain are then converted into a system of equations of motion with nodal positions as unknowns. Failure criteria and possible combinations of ‘connection’ breakage are incorporated to model the occurrence of damage. A practical contact algorithm is also developed to describe the contact interactions between cellular materials and rigid bodies. Simulations for normal and oblique impacts of rigid rectangular, cylindrical and wedge‐tipped impactors on crushable foam blocks are presented to substantiate the validity of the model. The generally good correlation between the numerical and experimental results demonstrates that the proposed numerical approach is able to model the impact response of the crushable foam. However, some limitations in modelling crack propagation in oblique impacts by a rigid impactor on foam blocks are observed. Copyright © 2001 John Wiley & Sons, Ltd.     

微孔结构对PMI泡沫准静态压缩性能的影响

基于BBC点集建立了聚甲基丙烯酰亚胺(PMI)闭孔泡沫的Kelvin十四面体模型和Laguerre模型,并采用有限元方法研究了其在准静态载荷作用下的压缩性能。分析了孔径大小、泡孔体积离散系数对压缩弹性模量、初始峰值应力和能量吸收能力的影响。结果表明:Kelvin十四面体模型可以较好地预测PMI泡沫的压缩弹性模量和峰值应力;在相同相对密度条件下,小孔径泡沫的初始峰值应力和能量吸收能力均高于大孔径泡沫,而压缩弹性模量则低于大孔径泡沫;随着泡孔体积离散系数的增大,闭孔PMI泡沫压缩弹性模量、初始峰值应力和能量吸收能力均减小。     

多孔材料性能模型研究3:数理推演

基于三维网状多孔材料的八面体结构模型,本文介绍了多孔材料基本物理、力学性能数理关系的推演过程。此过程覆盖了多孔材料的单向拉伸、多向拉压、传导性和疲劳性能等方面。重点描述了多孔材料内部构成的等效电路、多孔材料单向拉伸的准刚体结构受力模型和变形体结构受力模型,在此基础上讨论了压缩强度问题,并对双向拉伸和三向拉压的有关数理关系展开推演和分析。根据本八面体模型,多孔材料在弯曲等非直接拉压受力形式下的力学性能数理关系,同样可由单向拉压的推演而获得。     

多孔金属材料制备方法

本文概述了多孔金属材料的典型和特点，着重介绍了该材料的各种制备方法，以期提供一些优化组合生产工艺的线索。     

聚乙烯包装薄膜形变性能与微观结构的研究

采用拉伸实验，研究形变速率对聚乙烯包装薄膜力学性能的影响。采用Ｘ射线衍射方法，分析聚乙烯薄膜形变后微观结构的变化，得到了形变后材料内部的微晶尺寸和点阵畸变值。     

Topological optimization for the design of microstructures of isotropic cellular materials

The aim of this study was to design isotropic periodic microstructures of cellular materials using the bidirectional evolutionary structural optimization (BESO) technique. The goal was to determine the optimal distribution of material phase within the periodic base cell. Maximizing bulk modulus or shear modulus was selected as the objective of the material design subject to an isotropy constraint and a volume constraint. The effective properties of the material were found using the homogenization method based on finite element analyses of the base cell. The proposed BESO procedure utilizes the gradient-based sensitivity method to impose the isotropy constraint and gradually evolve the microstructures of cellular materials to an optimum. Numerical examples show the computational efficiency of the approach. A series of new and interesting microstructures of isotropic cellular materials that maximize the bulk or shear modulus have been found and presented. The methodology can be extended to incorporate other material properties of interest such as designing isotropic cellular materials with negative Poisson's ratio.     

多孔材料性能模型研究2:实验验证

在三维网状多孔材料"八面体结构模型"及其系列基本物理、力学性能相关数理模型和表征方式基础上,本文对传导和拉伸等若干性能指标的数理关系验证进行了综述。重点讨论了数理关系的实践性、修正系数的合理性、对计算结果的影响、对应致密体的许用应力取值和塑性指数取值等问题。按照这种数理关系,通过多孔产品孔率等基本参量即可计算其电阻率等性能指标,实验结果证明了其可行性。本方法可以优越于有限元等复杂计算。     

多孔材料性能模型研究1:数理关系

三维网状多孔材料是一类优秀的工程材料,其用途覆盖能源、生物、航空航天、环境保护、交通运输等诸多领域。本文作者根据三维网状多孔材料的结构特征,提出了综合简化的八面体结构模型,并在此基础上获得了该材料的系列性能关系。本文综合介绍了该模型及此类材料的基本物理、力学性能数理关系,从单向拉伸到多向拉压,以及传导性能和比表面积等。对该简化结构模型的根源、特点等进行了比较全面的描述,同时与同类模型进行了对比分析,并对不同性能模型及其性能关系进行了逐一诠释,其中代表性的问题有多孔体承载时涉及的孔棱细梁假设、孔棱弯曲、承载单元约束力,以及拉压性能关系中涉及的修正系数、塑性指数取值等。经实验验证该模型具有良好的实用性。     

Microstructure and XRD analysis of FSW joints for copper T2/aluminium 5A06 dissimilar materials

Copper (T2) and aluminium alloy (5A06) were welded by friction stir welding (FSW). The microstructure, mechanical properties and phase constituents of FSW joints were studied by metallography, tensile testing machine and X-ray diffraction. The results indicated that the high quality weld joint could be obtained when tool rotational speed is 950 rpm, and travel speed is 150 mm/min. The maximum value of tensile strength is about 296 MPa. The metal Cu and Al close to copper side in the weld nugget (WN) zone showed a lamellar alternating structure characteristic. However, a mixed structure characteristic of Cu and Al existed in the aluminium side of weld nugget (WN) zone. There were no new Cu-Al intermetallic compounds in the weld nugget zone.     

A nonparametric model of random uncertainties for reduced matrix models in structural dynamics

Random uncertainties in finite element models in linear structural dynamics are usually modeled by using parametric models. This means that: (1) the uncertain local parameters occurring in the global mass, damping and stiffness matrices of the finite element model have to be identified; (2) appropriate probabilistic models of these uncertain parameters have to be constructed; and (3) functions mapping the domains of uncertain parameters into the global mass, damping and stiffness matrices have to be constructed. In the low-frequency range, a reduced matrix model can then be constructed using the generalized coordinates associated with the structural modes corresponding to the lowest eigenfrequencies. In this paper we propose an approach for constructing a random uncertainties model of the generalized mass, damping and stiffness matrices. This nonparametric model does not require identifying the uncertain local parameters and consequently, obviates construction of functions that map the domains of uncertain local parameters into the generalized mass, damping and stiffness matrices. This nonparametric model of random uncertainties is based on direct construction of a probabilistic model of the generalized mass, damping and stiffness matrices, which uses only the available information constituted of the mean value of the generalized mass, damping and stiffness matrices. This paper describes the explicit construction of the theory of such a nonparametric model.     

A strain energy model for the prediction of the effective coefficient of thermal expansion of composite materials

In this paper, a strain energy model is developed for the prediction of the effective coefficient of thermal expansion (CTE) of composite materials. This model is based on the relationship established between the strain energy of the microstructure and that of the homogenized equivalent model under specific thermo-elastic boundary conditions. Expressions in closed-form are derived for the effective CTE in terms of the strain energy and effective elastic tensor. Different kinds of composites are tested to validate the model. Representative unit cells with specific boundary conditions are used to evaluate effective CTEs that are compared with available results obtained numerically and experimentally.     

Ordinary Portland Cement composition for the optimization of the synergies of supplementary cementitious materials of ternary binders in hydration processes

The synergistic effects of using several supplementary cementitious materials (SCMs), such as Blast Furnace Slags plus Limestone Filler or Fly Ashes, depend on the OPC composition. When using an OPC which is poor in C₃A and alkalis in ternary formulations, a similar initial strength gain to that of a plain OPC is detected and at longer hydration ages, the formation of monocarboaluminate, hemicarbonate and hydrotalcite instead of monosulphate can be seen. If an OPC with a higher C₃A content and alkalis is used with SCMs, the higher availability of Al causes the early formation of monocarboaluminate and a lower initial strength gain. At longer hydration times, in ternary blends with both OPCs, the mechanical strengths are higher and the C-S-H gels formed are richer in Al and poorer in C/S ratio with a subsequent lowering of the alkali content in the pore solution when compared to that in plain OPC.     

An adaptive material point method coupled with a phase-field fracture model for brittle materials

In this study, a new adaptive method for crack propagation analysis is developed by using the material point method coupled with a phase-field fracture model for brittle materials. A background grid of material particles is adaptively refined based on the amount of material damage to resolve the length scale in the phase-field evolution equation. A division process of the material particles associated with the refined background cells is also performed to increase the resolution of solutions near the crack tip. The effectiveness and validity of the proposed method is assessed through several numerical examples for crack propagation in brittle materials.     

Polycrystal models for the analysis of intergranular crack growth in metallic materials

In polycrystal materials the intergranular decohesion is one important damage phenomena that leads to microcrack initiation. The paper presents a mesoscale model, which is focused on the brittle intergranular damage process in metallic polycrystals. The model reproduces the crack initiation and propagation along cohesive grain boundaries between brittle grains. An advanced Voronoi algorithm is applied to generate polycrystal material structures based on arbitrary distribution functions of grain size. Therewith, the authors are more flexible to represent realistic grain size distributions. The polycrystal model is applied to analyze the crack initiation and propagation in statically loaded samples of aluminium on the mesoscale without the necessity of initial damage definition.     

Explicit formulations of tangent stiffness tensors for isotropic materials

A compact explicit expression for the tangent stiffness tensor is presented. Throughout the analysis, the formulation holds for general isotropic elastic materials and does not require solving eigenvector problems. On the theoretical side, a very simple solution of a tensor equation is obtained. Then the expressions for the derivatives of general symmetric isotropic tensor functions of a symmetric tensor are developed. On the computational side, particular attention is given to the consideration of the special case, Green elastic materials, in which the strain energy does not admit a closed‐form expression in terms of principal invariants. Finally, a simple formulation of the tangent stiffness tensor for Ogden material model is supplied. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical strategy for unbiased homogenization of random materials

This paper presents a numerical strategy that allows to lower the costs associated to the prediction of the value of homogenized tensors in elliptic problems. This is performed by solving a coupled problem, in which the complex microstructure is confined to a small region and surrounded by a tentative homogenized medium. The characteristics of this homogenized medium are updated using a self‐consistent approach and are shown to converge to the actual solution. The main feature of the coupling strategy is that it really couples the random microstructure with the deterministic homogenized model, and not one (deterministic) realization of the random medium with a homogenized model. The advantages of doing so are twofold: (a) the influence of the boundary conditions is significantly mitigated, and (b) the ergodicity of the random medium can be used in full through appropriate definition of the coupling operator. Both of these advantages imply that the resulting coupled problem is less expensive to solve, for a given bias, than the computation of homogenized tensor using classical approaches. Examples of 1‐D and 2‐D problems with continuous properties, as well as a 2‐D matrix‐inclusion problem, illustrate the effectiveness and potential of the method. Copyright © 2013 John Wiley & Sons, Ltd.     

Model order reduction for hyperelastic materials

In this paper, we develop a novel algorithm for the dimensional reduction of the models of hyperelastic solids undergoing large strains. Unlike standard proper orthogonal decomposition methods, the proposed algorithm minimizes the use of the Newton algorithms in the search of non‐linear equilibrium paths of elastic bodies. The proposed technique is based upon two main ingredients. On one side, the use of classic proper orthogonal decomposition techniques, that extract the most valuable information from pre‐computed, complete models. This information is used to build global shape functions in a Ritz‐like framework. On the other hand, to reduce the use of Newton procedures, an asymptotic expansion is made for some variables of interest. This expansion shows the interesting feature of possessing one unique tangent operator for all the terms of the expansion, thus minimizing the updating of the tangent stiffness matrix of the problem. The paper is completed with some numerical examples in order to show the performance of the technique in the framework of hyperelastic (Kirchhoff–Saint Venant and neo‐Hookean) solids. Copyright © 2009 John Wiley & Sons, Ltd.