Yield and buckling behavior of Kelvin open-cell foams subjected to uniaxial compression

This study analyzes the yield and buckling behavior of Kelvin open-cell foams subjected to uniaxial compression. A homogenization theory of the updated Lagrangian type is applied to cubic unit cells and cell aggregates in the Kelvin foam model. Macroscopic instability and microscopic bifurcation are thus incrementally examined under uniaxial compression. The analysis is performed by taking into account the non-uniformity of strut cross-sectional areas and the strain hardening-softening behavior of struts that were observed in experiments on open-cell 6101-T6 aluminum alloy foams. It is shown that macroscopic instability primarily occurs as a consequence of the strain hardening-softening behavior of struts. It is further shown that the macroscopic instability stress obtained has (3/2)th power dependence on relative density as predicted in the Gibson-Ashby relation.     

Homogenized elastic-viscoplastic behavior of plate-fin structures at high temperatures: Numerical analysis and macroscopic constitutive modeling

In this study, homogenized elastic-viscoplastic behavior of an ultra-fine plate-fin structure fabricated for compact heat exchangers is investigated. First, the homogenized behavior is numerically analyzed using a fully implicit mathematical homogenization scheme of periodic elastic-inelastic solids. A power-law creep relation is assumed to represent the viscoplasticity of base metals at high temperatures. The plate-fin structure is thus shown to exhibit significant anisotropy as well as noticeable compressibility in both the elastic and viscoplastic ranges of the homogenized behavior. Second, a non-linear rate-dependent macroscopic constitutive model is developed using the quadratic yield function proposed for anisotropic compressible plasticity. The resulting constitutive model is shown to be successful for simulating the anisotropy, compressibility, and rate dependency in the homogenized behavior in multi-axial stress states.     

A morphological elastic model of general hexagonal columnar structures

A general three-dimensional (3D) anisotropic hexagonal model of columnar structure with non-uniform strut morphology is developed. This model covers several types of cellular structure such as two-dimensional (2D) hexagonal and square honeycombs, and 3D hexagonal and rhombic cellular materials of rod-like columnar structure. The effective elastic constants are determined taking account of bending, axial, and shear deformations of the struts. Unlike the theoretical work of other investigators for 2D honeycombs, considering bending, axial and shearing deformations of struts, the present model not only produces transverse isotropy for regular hexagonal columnar structure but also provides a consistent Poisson's ratio when applied to a square honeycomb. The effect of tapered strut morphology on the elastic properties of cellular structures is investigated. For the general hexagonal columnar structures, the bending compliance is the dominant function for the in-plane elastic constants of 2D and 3D structures (excluding the in-plane shear modulus of rhombic structures) and the out-of-plane shear moduli of 3D structures, but the axial compliance is dominant for the in-plane shear modulus of 2D and 3D rhombic structures and the out-of-plane Young's modulus of 3D structures. For cellular materials with the same relative density, the presence of taper increases values of the effective Young's and shear moduli for which the bending compliance is dominant, but decreases those for which the axial compliance is dominant. It is found that the effective elastic properties of cellular materials are dependent not only on the relative density but also on strut morphology both in cross-section geometry and its variation along the strut length which the present model takes account of. These results illustrate the importance of the strut morphology in calculating the effective elastic properties of cellular materials.     

Micro- to macroscopic responses of a glass particle-blended polymer in the presence of an interphase layer

A multi-scale model which can be used to evaluate the interaction between a microstructure and the heterogeneous deformation behavior of ternary composites on the micro- to macroscopic scale has been developed based on the large deformation finite element homogenization method. Using four different interphases consisting of a rubber, two different types of polymer and an elastic material with intermediate stiffness of particle and matrix, the elasto-plastic behaviors of the composites have been confirmed to be markedly influenced by the interphase properties and the interphase with a stiffness well below that of the matrix shows a suitable effect on the micro- to macroscopic deformation behaviors of the composites. Therefore, a computational simulation has been performed for the present interphase to clarify the effects of the macroscopic strain ratio, interphase properties and particle volume fraction on macroscopic characteristics such as deformation resistance, elasticity modulus and yield stress, and on microscopic characteristics such as shear band pattern, mean stress in the matrix and normal stress on the particle surface. The results provide guidelines for selecting interphase properties and processing parameters to achieve desired overall composite characteristics.     

基于满应变准则的受应力约束三维弹性体拓扑优化

提出一种受应力约束三维弹性体的拓扑优化方法：修改的满应变法,即通过反熨迭代修改单元的弹性模量。使三维弹性体的每个单元均处于一种满应变的状态,然后删除弹性模量较低的单元,通过逐渐删除弹性模量较低的单元,使单元最大弹性模量逐渐接近于材料实际的弹性模量,同时单元的最大应力也逐渐接近于材料的许可应力,从而获得满足应力约束条件的三维弹性体的最优拓扑。同时引入结构描述数组的概念,很方便地实现单元的重新划分。数值结果表明该方法很有效,且具有很好的通用性和稳健性。     

The effect of strut geometry on the yielding behaviour of open-cell foams

A micromechanical analysis was carried out to investigate the effect of strut geometry on the yielding behaviour of open-cell foams. Different strut cross sections, in rectangular, circular and equilateral triangular shapes, were investigated. It was found that the strut geometry significantly affects the plastic-yielding behaviour of open-cell foams. The shape of the plastic-yield surface was found to depend not only on relative density but also on the cross-sectional shape of the struts. Numerical results show that even though the material of the struts is perfectly plastic, open-cell foams with asymmetrical sectional struts will exhibit different tensile and compressive collapse strength.     

Thermoelastic Characteristics of a Composite with Anisotropic Platelike Inclusions

A mathematical model is constructed describing the thermomechanical action of the elements of a composite structure (platelike inclusion and matrix particles) and isotropic elastic medium with the required thermomechanical characteristics. The model is used at the first stage to obtain the matrix relations by the self-consistent method to find the elastic modulus of the composite. At the second stage, it is used to determine the temperature coefficient of linear expansion. Using the variation approach for the composite considered, the two-way estimates of the volumetric elasticity modulus, shearing modulus, and temperature coefficient of linear expansion are determined. The estimated dependences presented allow forecasting the thermoelastic characteristics of the composite, which is reinforced with the anisotropic platelike inclusions (including in the form of nanostructural elements).     

Prediction of anisotropic material behavior based on multiresolution continuum mechanics in consideration of a characteristic length scale

New advanced materials have received more attention from many scientists and engineers because of their outstanding chemical, electrical, thermal, optical, and mechanical properties. Since the design of advanced material by experiments requires high cost and time, numerical approaches have always been of great interest. In this paper, finite element analysis of anisotropic material behavior has been carried out based on a multiresolution continuum theory. Gurson-Tvergaard-Needleman (GTN) damage model has been applied as a constitutive model at macroscale. Effects of plastic anisotropy on deformation behavior are assessed using Hill??s 48 yield function for anisotropic material and von Mises yield function for isotropic material, respectively. The material parameters for both isotropic and anisotropic damage models have systematically been determined from microstructure through unit cell modeling. The newly proposed linear approximation of local velocity gradient resolved the underdetermined problem of the previous homogenization process. Anisotropic material behaviors of a tensile specimen have been investigated by the proposed multiresolution continuum theory.     

Elastohydrodynamic lubrication analysis of a functionally graded layered bearing surface,with particular reference to 'cushion form bearings' for artificial knee joints

Elastohydrodynamic lubrication of a functionally graded layered (FGL) bearing surface, whose elastic modulus increases with depth from the bearing surface, was investigated in this study. The finite difference method was employed to solve the Reynolds equation, simultaneously with the elasticity equation of the bearing surface, under circular point contacts. The finite element method was adopted to solve the elasticity equation for the FGL bearing surface. The displacement coefficients thus obtained were used to calculate the elastic deformation of the bearing surface, required for the elastohydrodynamic lubrication analysis. Good agreement of the predicted film thickness and pressure distribution was obtained, between the present method and a previous study for a single layered bearing surface with a uniform elastic modulus. The general numerical methodology was then applied to an FGL bearing surface with both linear and exponential variations in elastic modulus, with particular reference to the 'cushion form bearing' for artificial knee joints. The predicted film thickness and pressure distribution were shown to be quite close to those obtained for a single layer under typical operating conditions representative of artificial knee joints, provided that the elastic modulus of the single layer was chosen to be the average elastic modulus of the graded layer.     

Constitutive modeling of polymeric foams having a four-parameter modulus function with strain rate sensitivity

Journal of Mechanical Science and Technology - A constitutive model of polymeric foams having a four-parameter modulus function is suggested. The modulus function consists of two linear functions...     

Computational evaluation of strain-rate-dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining

The molecular chain network model for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior are used to derive a constitutive equation for rubber. The new eight-chain-like model contains eight standard models consisting of Langevin springs and dashpot to account for the interaction of chains with their surroundings. Monotonic and cyclic deformation behavior of rubber with relaxation under different strain rates have been examined. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes. The validity of the results is checked through comparison with experimental results. The deformation behaviors of a plane strain rubber unit cell containing carbon-black (CB) under monotonic and cyclic straining are investigated by computational simulation using the proposed constitutive equation and homogenization method. The results reveal the substantial enhancement of the resistance of CB-filled rubber to macroscopic deformation, which is caused by the marked orientation hardening due to the highly localized deformation of rubber. The role of strain rate sensitivity on such characteristic deformation behaviors as increases in the resistance to deformation, hysteresis loss, and the effects of the distribution morphology and the volume fraction of CB on the deformation behavior is clarified. The increases in the volume fraction and in the aggregation of the distribution of CB substantially raise the resistance to deformation and hysteresis loss.     

Homogenized properties of elastic–viscoplastic composites with periodic internal structures

A homogenization theory for elastic–viscoplastic composites with periodic internal structures is developed in rate and incremental forms by considering unit cells subjected to macroscopically uniform stress and strain. The theory enables us to incrementally compute the macroscopic as well as the microscopic stress and strain states in nonlinear time-dependent periodic composites. The theory is effective for problems in which the history of either macro-strain or macro-stress, or a combination of them, is prescribed as a function of time. As applications of the theory, transverse and off-axial deformation problems of metal matrix composites reinforced unidirectionally with continuous fibers are analyzed to discuss the effects of fiber arrangement and orientation on the macroscopic deformation behavior.     

A method of predicting macroscopic yield strength of polycrystalline metals subjected to plastic forming by micro-macro de-coupling scheme

We introduce a method of predicting the macroscopic yield strength of polycrystalline metals subjected to plastic forming, which hinges on the reliability of the micro-macro decoupling scheme for solving the corresponding two-scale boundary value problem. A polycrystalline aggregate composed of several crystal grains is adopted as a periodic microstructure, namely unit cell, and is regarded as a numerical specimen for numerical material tests (NMTs) based on the homogenization theory. The NMTs are conducted to identify the material parameters of the assumed approximate macroscopic constitutive model and followed by the de-coupled macro-scale analysis to simulate the macro-scale forming process. We then conduct the de-coupled micro-scale analysis by applying the resulting macroscopic deformation histories to the microstructures associated with the macroscopic points of interest in order to obtain the numerical specimens after plastic forming. Finally, the NMTs are conducted on the prepared specimens to evaluate the macroscopic post-forming yield strengths. We validate the proposed method by taking the three-step forming process as an example of macroscopic plastic forming. The validation of the method is made in comparison with the results with those obtained by the equivalent two-scale analysis with the coupling scheme. To demonstrate the capability and promise of the proposed method for practical applications, we also present an numerical example of the rolling process that causes the texture development in crystal grains.     

A constitutive model for polyurethane foam with strain rate sensitivity

The present work investigates the strain rate dependent behavior of polyurethane foams and formulates a new constitutive model in order to improve the fit of the experimental data at various strain rates. The model has seven parameters that are decided by quasi-static compression tests at two strain rates. Two models for low and high density polyurethane foams are shown to give stress strain relation at various strain rates. Dynamic compression tests were carried out to give stress strain data at high strain rate and the results are compared with those of the constitutive model.     

Effective mechanical behavior of hyperelastic honeycombs and two-dimensional model foams at finite strain

The aim of the present study is the analytical and numerical determination of the effective stress–strain behavior of solid foams made from hyperelastic materials in the finite strain regime. For the homogenization of the microstructure, a strain energy-based concept is proposed which assumes macroscopic mechanical equivalence of a representative volume element for the given microstructure with a similar homogeneous volume element if the strain energy of both volume elements is equivalent, provided that the volume average of the deformation gradient is equal for both volume elements. The concept is applied to an analysis of hyperelastic solid foams using a two-dimensional model. The effective stress–strain behavior is analyzed under uniaxial and biaxial loading conditions in the tensile and in the compressive range as well as under simple shear deformation. It is observed that the effective mechanical behavior of cellular solids at infinitesimal and finite deformation is essentially different on both, the quantitative and the qualitative level.     

Polycrystalline behavior analysis of pure magnesium by the homogenization method

In this study, mechanical behaviors of pure magnesium polycrystals are numerically investigated. The homogenization method, which combines the crystal and macroscopic scales, is introduced to include the effect of crystalline scale behaviors. The polycrystal plasticity model modified for pure magnesium, in which twinning is considered as asymmetric slip-like deformation, is utilized as a constitutive equation. Within this framework, numerical convergence analyses are conducted, and a representative volume element to present realistic deformation of pure magnesium is investigated. Second, polycrystalline behaviors of pure magnesium are investigated. The present approach is shown to reproduce the typical phenomena induced by crystalline scale structure in pure magnesium: nonuniform strain distribution, asymmetric crystal lattice orientation, strength differential effect, and strongly anisotropic initial and subsequent yield surfaces.     

DFT-based FEM analysis of nonlinear effects on indentation process in diamond crystal

We apply a new framework of a finite-element method (FEM) analysis with constitutive relations based on density functional theory (DFT), as an efficient method to characterize the nonlinear and anisotropic elastic deformation of single-crystal diamond. In our scheme, the stress-strain relations are obtained during FEM analysis on the fly based on the plane-wave-based DFT total-energy calculations and their numerical database is simultaneously constructed, which enables us to obtain high-precision stress without any empirical parameters even under finite strained conditions. To check its validity and accuracy, the shear deformation behavior of diamond crystal is analyzed under the strained condition. Then we examine the nonlinear effects on the indentation deformation of diamond single crystal, by comparing the results from the DFT-based constitutive relations with those from the linear elastic ones.     

一种高聚物的高低温本构模型

随着高聚物在汽车工业中的应用日益增加,高聚物的性能对汽车的安全性有着不容忽视的影响,尤其是高聚物在高低温下的力学性能差异巨大。因此,结合国内外学者的理论研究与试验基础以及实际使用要求,推导出高聚物在高低温下的三参数本构方程。该本构模型与材料力学性能的基本特征量建立关系,直接由弹性模量E、屈服强度δ_y、应变ε三参数表示,并包含弹性模量、屈服强度与温度的双曲关系。该模型通过常温应力应变试验数据,及高低温下至少4个屈服强度与弹性模量的试验数据即可实现高聚物在高低温下的力学性能预测,极大降低由于高低温引伸仪的使用而造成的试验难度与强度。本构模型的可行性与有效性通过多种高聚物材料的试验数据得到验证,该本构模型可作为获取高聚物高低温力学性能的有效手段。     

A simple non-linear constitutive equation for elastohydrodynamic oil films

In this paper a hypothetical constitutive relation for EHL oil films is proposed which combines a linear elastic response with a non-linear shear thinning viscous response. This model reduces to a linear Maxwell fluid for small strains. It is shown that provided the recoverable elastic strains are kept small (<0.3), which is generally the case for EHL contacts, the ambiguity of stress rate usually encountered with large total strains in viscoelasticity can be avoided. Hence this proposed constitutive law provides a simple Theologically acceptable basis for interpreting large strain EHD traction experiments.     

悬索式跨越架用纤维绳索非线性本构关系试验研究

悬索式跨越架在跨越电力线路施工中应用广泛,其承载索及封网绳多采用超高分子量聚乙烯纤维绳索和聚酯纤维绳索.由于进行悬索式跨越架动力学仿真计算纤维绳索所涉及的非线性本构关系尚无公开资料,各单位在进行仿真计算时采用弹性模量固定值来替代非线性应力—应变关系曲线,导致计算结果与实际情况不符.针对上述问题,对这两种常用规格的纤维绳...