Multi-scale analysis of the early damage mechanics of ferritized ductile iron

A multiscale computational homogenization method for the modeling of hydro-mechanical coupling problem for quasi-brittle materials is developed. The present method is based on an asymptotic expansion homogenization combined with the semi-concurrent finite element modelling approach. Modified periodic boundary conditions and a molecular dynamics (MD) based inclusion or filler generation procedure are devised for the hydro-mechanical coupling problem. A modified elastic damage constitutive model and a damage induced permeability law have been developed for the hydraulic fracturing. The statistical convergence of the microscale representative volume element (RVE) model regarding the RVE characteristic size is studied. It was found that the RVE characteristic size is determined by both the mechanical and hydraulic properties of the RVE simultaneously. The present method is validated by the experimental results for brittle material. The damage zone and crack propagation path captured by the present method is compared with the experimental results (Chitrala et al. in J Pet Sci Eng 108:151–161, 2013). The results show that the present method is an effective for the modelling of hydro-mechanical coupling for brittle materials.     

Scale transition and enforcement of RVE boundary conditions in second‐order computational homogenization

Formulation of the scale transition equations coupling the microscopic and macroscopic variables in the second‐order computational homogenization of heterogeneous materials and the enforcement of generalized boundary conditions for the representative volume element (RVE) are considered. The proposed formulation builds on current approaches by allowing any type of RVE boundary conditions (e.g. displacement, traction, periodic) and arbitrary shapes of RVE to be applied in a unified manner. The formulation offers a useful geometric interpretation for the assumptions associated with the microstructural displacement fluctuation field within the RVE, which is here extended to second‐order computational homogenization. A unified approach to the enforcement of the boundary conditions has been undertaken using multiple constraint projection matrices. The results of an illustrative shear layer model problem indicate that the displacement and traction RVE boundary conditions provide the upper and lower bounds of the response determined via second‐order computational homogenization, and the solution associated with the periodic RVE boundary conditions lies between them. Copyright © 2007 John Wiley & Sons, Ltd.     

Transverse elastic shear of auxetic multi re-entrant honeycombs

The paper describes the transverse shear properties of a novel centresymmetric honeycomb structure evaluated using analytical and finite element models. The cellular structure features a representative volume element (RVE) geometry allowing in-plane auxetic (negative Poisson’s ratio) deformations, and multiple topologies to design the honeycomb for multifunctional applications. The out-of-plane properties are calculated using a theoretical approach based on Voigt and Reuss bounds. The analytical models are validated using a full scale Finite Element technique to simulate transverse shear tests, a quarter FE of the RVE with periodic shear conditions and an FE homogenisation method for periodic structures. The comparison between the analytical and numerical models shows good convergence between the different set of results, and highlights the specific deformation mechanism of the multi re-entrant honeycomb cell.     

Scaling of honeycomb compressive yield stresses

In this study, the compressive yield stresses of phenolic-dipped Nomex^® rings were scaled and correlated to honeycomb core. A honeycomb-scaling factor and geometric end constraint factor were found to relate the rings and core through the relative yield stresses and their physical dimensions and properties of the honeycomb materials. The compressive properties of the Nomex rings were also investigated using both a model and a commercial phenolic honeycomb dip resin. The Nomex rings manufactured from the model resin were found to have higher compressive properties. These properties were attributed to the higher fracture toughness of the resin, and both resins were found to accurately scale from rings to core with the honeycomb-scaling factor. Ultimately, this research can be used to innovate and efficiently characterize the compressive properties of different honeycomb webs and dip resins without having to make the significant investment of time and resources associated with large scale honeycomb testing.     

The derivation of equivalent constitutive equations of honeycomb structures by a two scale method

This paper evaluates the equivalent transverse shear and in-plane moduli of honeycomb cellular structures. The derivation is based upon a two scale method for the homogenization of periodic media. The equivalent two dimensional constitutive equations are evaluated analytically in terms of their geometry and material properties. The present results compare well with some of the existing analytical results obtained by conventional approaches and show the errors of some of the earlier results. The present method is a systemetic and rational technique for the homogenization of periodically inhomogeneous media. It allows us to derive the equivalent mechanical properties of honeybombs systemetically for the analysis and design of cellular structures of honeycomb. The structural efficiency of honeycombs will also be discussed.This work was supported by the GRC of Hong Kong Under Grant No. HKUST 019/91     

A comparison of homogenization and standard mechanics analyses for periodic porous composites

Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as , goes to zero. However, many composites are locally periodic with finite . The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodic porous composites with finite . Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. Howver, for two- and three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic composites the effective material properties predicted by standard mechanics approaches using multiple cell RVEs converged to the homogenization predictions using one cell. In addition, homogenization estimates of local strain energy density were within 30% of direct analyses while standard mechanics approaches generally differed from direct analyses by more than 70%. These results suggest that homogenization theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and is finite.     

Critical buckling load of paper honeycomb under out‐of‐plane pressure

Two out‐of‐plane buckling criteria for paper honeycomb are proposed by analysing the structure properties and the collapse mechanism of paper honeycomb: these are based on the peeling strength and ring crush strength of the chipboard wall. Taking into account the orthotropic, initial deflection and large deflection properties of the chipboard wall, the two new mechanical models and the calculation methods are developed to represent the out‐of‐plane critical load of paper honeycomb. Theoretical calculations and test results show that the models are suitable for describing the collapse mechanism of paper honeycomb. The peeling strength and ring crush strength determine the critical buckling load of paper honeycomb in different stretch phases. The out‐of‐plane critical buckling load can be predicted when the two models are integrated. Copyright © 2005 John Wiley & Sons, Ltd.     

A non‐linear programming approach to kinematic shakedown analysis of composite materials

Using a Representative volume element (RVE) to represent the microstructure of periodic composite materials, this paper develops a non‐linear numerical technique to calculate the macroscopic shakedown domains of composites subjected to cyclic loads. The shakedown analysis is performed using homogenization theory and the displacement‐based finite element method. With the aid of homogenization theory, the classical kinematic shakedown theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. By means of non‐linear mathematical programming techniques, a finite element formulation of kinematic shakedown analysis is then developed leading to a non‐linear mathematical programming problem subject to only a small number of equality constraints. The objective function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load of a composite is then obtained. An effective, direct iterative algorithm is proposed to solve the non‐linear programming problem. The effectiveness and efficiency of the proposed numerical method have been validated by several numerical examples. This can serve as a useful numerical tool for developing engineering design methods involving composite materials. Copyright © 2005 John Wiley & Sons, Ltd.     

A homogenization technique for heat transfer in periodic granular materials

A homogenization technique is proposed to simulate the thermal conduction of periodic granular materials in vacuum. The effective thermal conductivity (ETC) and effective volumetric heat capacity (EVHC) can be obtained from the granular represent volume element (RVE) via average techniques: average heat flux and average temperature gradient can be formulated by the positions and heat flows of particles on the boundaries of the RVE as well as of the contact pairs within the RVE. With the thermal boundary condition imposed on the border region around the granular RVE, the ETC of the granular RVE can be computed from the average heat flux and average temperature gradient obtained from thermal discrete element method (DEM) simulations. The simulation results indicate that the ETC of the granular assembly consisting of simple-cubic arranged spheres coincides with the theoretical prediction. The homogenization technique is performed to obtain the ETC of the RVE consisting of random packed particles and the results exhibit the anisotropy of the thermal conduction properties of the RVE. Both the ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials with finite element analyses, which give the similar results of temperature profile and conduction properties as the DEM simulations.     

基于RVE单元的藏式古建石砌体均质化研究

在普通砖石砌体结构方面的均质化研究已经较为完善,而在构造、材料存在随机性的古建筑砌体结构方面的均质化研究相对欠缺。该文以有限尺度测试窗法为基础,提出了一种选择砌体结构代表性体积单元(RVE单元)的方法,并与试验和传统有限元模拟结果对比,验证了所提方法的可行性。在此基础上,该文进行了藏式古建石砌体结构RVE单元的选择,探讨了RVE单元的尺寸大小和所包含的组元分布对等效模量的影响,并基于所选RVE单元建立了藏式石砌体结构的均质化模型和整体式模型。结果表明:该选择方法适用于周期性和准周期性砌体结构,能选出与完整结构力学性能接近的RVE单元。随着RVE单元尺寸变大,其Voigt、Reuss等效模量会逐渐向完整结构的模量收敛,呈现先快后慢的变化趋势;组元分布的不同会改变等效模量的收敛程度,但在较大尺寸的RVE单元上,组元分布的影响将被体积造成的影响抵消。该文所建均质化模型能代替传统有限元模型进行局部结构的分析,并给出藏式古建石砌体结构的应力分布规律;所建整体模型能代替传统有限元模型,较为精确模拟结构整体的宏观变形。     

Compressive and flexural properties of biomimetic integrated honeycomb plates

The characteristics of honeycomb plates composed of an upper and lower lamination are employed to create a novel single-sided bonded honeycomb plate (SBHP) design, and the compressive and flexural properties of these biomimetic integrated honeycomb plates are investigated. The results demonstrate that even during the fracturing of the honeycomb plates (honeycomb core), no abrupt compression paralysis occurs (which would cause the load to decrease rapidly); furthermore, our honeycomb plates exhibit superior compressive properties compared to biomimetic sandwich plates manufactured using Zhang’s needle-injection method. The interfacial bonding surface and bonding quality have no significant effect on the flexural stiffness but do affect the failure modes and flexural failure strength of the honeycomb plates. The ultimate failure of the biomimetic integrated honeycomb without a bonding layer between the panel–core layers is determined by the material strength itself; therefore, the honeycomb possesses good mechanical properties. This experimental study confirms, for the first time, the effectiveness of the biomimetic integrated honeycomb structure manufacturing method.     

Experimental and numerical study of the elastic properties of PMI foams

The elastic properties of polymethacrylimide (PMI) foams were investigated experimentally and numerically. Standard tests were carried to measure the mechanical properties of ROHACELL^? WF and RIST grades foams. The tetrakaidekahedral unit cell was adopted to generate a 3D representative volume element (RVE) for the microstructure of PMI foams. It is assumed that the RVE represents the foam within the framework of elasticity. The RVE models thus created were analyzed with periodic boundary conditions to obtain the elastic properties of PMI foams by using finite element analysis (FEA). The numerical results were compared with the experimental data and the prediction of existing theoretical models, and the proposed model was found to give the best prediction for the effective modulus of PMI foams. Parameter studies were also carried out using the RVE models to investigate the effect of the foam cell size and cell thickness on the effective modulus of PMI foams.     

Experimental Analysis and Modeling of the Crushing of Honeycomb Cores

In the aeronautical field, sandwich structures are widely used for secondary structures like flaps or landing gear doors. The modeling of low velocity/low energy impact, which can lead to a decrease of the structure strength by 50%, remains a designers main problem. Since this type of impact has the same effect as quasi-static indentation, the study focuses on the behavior of honeycomb cores under compression. The crushing phenomenon has been well identified for years but its mechanism is not described explicitly and the model proposed may not satisfy industrial purposes. To understand the crushing mechanism, honeycomb test specimens made of Nomex, aluminum alloy and paper were tested. During the crushing, a CCD camera showed that the cell walls buckled very quickly. The peak load recorded during tests corresponded to the buckling of the common edge of three honeycomb cells. Further tests on corner structures to simulate only one vertical edge of a honeycomb cell show a similar behavior. The different specimens exhibited similar load/displacement curves and the differences observed were only due to the behavior of the different materials. As a conclusion of this phenomenological study, the hypothesis that loads are mainly taken by the vertical edge can be made. So, a honeycomb core subjected to compression can be modeled by a grid of nonlinear springs. A simple analytical model was then developed and validated by tests on Nomex honeycomb core indented by different sized spherical indenters. A good correlation between theory and experiment was found. This result can be used to satisfactorily model using finite elements the indentation on a sandwich structure with a metallic or composite skin and honeycomb core.     

Scale‐related topology optimization of cellular materials and structures

The integrated optimization of lightweight cellular materials and structures are discussed in this paper. By analysing the basic features of such a two‐scale problem, it is shown that the optimal solution strongly depends upon the scale effect modelling of the periodic microstructure of material unit cell (MUC), i.e. the so‐called representative volume element (RVE). However, with the asymptotic homogenization method used widely in actual topology optimization procedure, effective material properties predicted can give rise to limit values depending upon only volume fractions of solid phases, properties and spatial distribution of constituents in the microstructure regardless of scale effect. From this consideration, we propose the design element (DE) concept being able to deal with conventional designs of materials and structures in a unified way. By changing the scale and aspect ratio of the DE, scale‐related effects of materials and structures are well revealed and distinguished in the final results of optimal design patterns. To illustrate the proposed approach, numerical design problems of 2D layered structures with cellular core are investigated. Copyright © 2006 John Wiley & Sons, Ltd.     

Mechanical behaviour of cellular core for structural sandwich panels

This paper deals with the analysis of the mechanical properties of the core materials for sandwich panels. In this work, the core is firstly a honeycomb and secondly tubular structure. This kind of core materials are extensively used, notably in automotive construction (structural components, load floors...). For this study, three approaches are developed: a finite element analysis, an analytical study and experimental tests. Structural members made up of two stiffs, strong skins separated by a lightweight core (foam, honeycomb, tube...) are known as sandwich panels. The separation of the skins by the core increases the inertia of the sandwich panel, the flexure and shear stiffness. This increase is obtained with a little increase in weight, producing an efficient structure to resist bending and buckling loads. A new analytical method to analyse sandwich panels core will be presented. These approaches (theoretical and experimental) are used to determine elastic properties and ultimate stress. A parameter study is carried out to determine elastic properties as a function of geometrical and mechanical characteristics of basic material. Both theoretical and experimental results are discussed and a good correlation between them is obtained.     

Failure behaviour of honeycomb sandwich corner joints and inserts

In nearly all sandwich constructions certain types of joints have to be used for assembly, but little is known about their failure behaviour. This paper deals with the investigation of the mechanical behaviour of three different corner joints as a right-angled connection of two sandwich panels and of two different potted inserts as a localised load introduction in Nomex^® honeycomb sandwich structures with glass fibre-reinforced composite skins. For this purpose, experimental test series were conducted including shear tests and bending tests of the corner joints and pull-out as well as shear-out tests of the threaded inserts. The failure mechanisms and sequences are described for each load case and the influence of the different designs and of the loading rate is discussed. Based on these characteristics, finite element simulation models were developed in LS-DYNA, which are able to represent the respective failure behaviours.     

Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores

The present study investigates the influences of representative volume element RVE mesh and material parameters, here cell wall elastic moduli, on the effective stiffness properties of three dimensional orthotropic honeycomb cores through strain driven computational homogenization in the finite element framework. For this purpose, case studies were carried out, for which hexagonal cellular RVEs were generated, meshed with eight node linear brick finite elements of varying numbers. Periodic boundary conditions were then implemented on the RVE boundaries by using one-to-one nodal match for the corresponding corners, edges and surfaces for the imposed macroscopic strains. As a novelty, orthotropic material properties were assigned for each cell wall by means of the transformation matrices following the cell wall orientations. Thereafter, simulations were conducted and volume averaged macroscopic stresses were obtained. Eventually, effective stiffness properties were obtained, through which RVE sensitivity analysis was carried out. The investigations indicate that there is a strong relation between number of finite elements and most of the effective stiffness parameters. In addition to this, cell wall elastic moduli also play critical role on the effective properties of the investigated materials.     

蜂窝集装箱地板结构优化设计及强度校核

研究了蜂窝地板在弯曲载荷作用下的失效形式,并基于失效因子建立了优化模型。根据地板结构的优化设计准则,以地板的高抗弯刚度、高强度要求、高固有频率和小质量为目标函数,以稳定性、屈曲极值、剪切强度和刚度为约束条件,构造了评价函数,得出了最优尺寸以及对应的力学性能参数。最后利用强度计算公式对该设计进行了校核,计算结果表明,优化后的蜂窝集装箱地板能满足使用要求。     

A micromechanical analysis of a local failure criterion for particle-reinforced composites

The present paper aims at predicting the ultimate mechanical properties of a particle-reinforced polymer using a micromechanical approach of a local failure criterion. The considered criterion includes both normal and shear stresses at the interface between the polymer matrix and the reinforcing material. In the case of rigid particles, a new closed-form expression of the interfacial stress concentration tensor is provided and simple analytical formula are proposed and compared for different homogenization schemes. A combination of these results with acoustic emission data allows the identification of the parameters involved in the local failure criterion. It has been shown that the predicted interfacial strength highly depends on the choice of a suitable homogenization scheme.     

锈蚀钢材偏心受压钢柱承载性能退化规律

为研究锈损对冷弯薄壁型钢短柱受压承载性能的影响,设计加工了6个轴压及6个绕强轴偏心受压短柱试件,首先通过拉伸试验,分析了材料力学性能与锈蚀程度间的关系,然后对试件进行承载力试验,分析其破坏模式、极限承载力及变形特征等特性,结果表明：锈损钢材的屈服、抗拉强度、弹性模量及伸长率均随锈蚀程度的增加呈线性下降趋势。锈损未使短柱试件的最终破坏模式发生变化,但随着偏心距的增大,试件由腹板局部屈曲变为以畸变屈曲为主的耦合破坏模式;在相同锈蚀率条件下,轴压试件的极限承载能力较偏压试件退化更明显。采用ABAQUS有限元软件对试件进行数值模拟,计算结果表明其能够较好的预测试件承载力及屈曲行为。