A micro-mechanical homogenisation model for masonry: Application to shear walls

An improved micro-mechanical model for masonry homogenisation in the non-linear domain, is proposed and validated by comparison with experimental and numerical results available in the literature. Suitably chosen deformation mechanisms, coupled with damage and plasticity models, can simulate the behaviour of a basic periodic cell up to complete degradation and failure. The micro-mechanical model can be implemented in any standard finite element program as a user supplied subroutine defining the mechanical behaviour of an equivalent homogenised material. This work shows that, with the proposed model, it is possible to capture and reproduce the fundamental features of a masonry shear wall up to collapse with a coarse finite element mesh. The main advantage of such homogenisation approach is obviously the possibility to simulate real complex structures while taking into consideration the arrangement of units and mortar, which would otherwise require impractical amount of finite elements and computer resources.     

基于固有耗散的材料疲劳性能快速评估方法

材料疲劳损伤的累积过程是一个伴随着温度变化的能量耗散过程. 相比于疲劳过程中试件的局部温升,固有耗散是材料能量变化的直接反映,与材料微观结构演化联系也更为紧密,因此以材料的固有耗散作为疲劳损伤指标具有更加明确的物理意义. 基于对试件表面温升的一维双指数回归,构建了一种材料固有耗散的计算模型,并在此基础上提出了一种快速评估材料疲劳性能的能量方法. 利用该能量方法,对FV520B 钢的疲劳性能进行了实验研究,并对实验结果进行了分析与对比,从而证明了该能量方法及计算模型的可行性和有效性.      

Finite element simulation of deformation behaviour of cellular rubber components

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using a porous hyperelastic material model within the framework of homogenisation method to consider pore volume fraction. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The finite element simulations are then followed by compression load tests to validate the material model.     

AN ENERGY APPROACH TO RAPIDLY ESTIMATE FATIGUE BEHAVIOR BASED ON INTRINSIC DISSIPATION

材料疲劳损伤的累积过程是一个伴随着温度变化的能量耗散过程. 相比于疲劳过程中试件的局部温升,固有耗散是材料能量变化的直接反映,与材料微观结构演化联系也更为紧密,因此以材料的固有耗散作为疲劳损伤指标具有更加明确的物理意义. 基于对试件表面温升的一维双指数回归,构建了一种材料固有耗散的计算模型,并在此基础上提出了一种快速评估材料疲劳性能的能量方法. 利用该能量方法,对FV520B 钢的疲劳性能进行了实验研究,并对实验结果进行了分析与对比,从而证明了该能量方法及计算模型的可行性和有效性.     

Sensitivity analysis of the thermomechanical response of welded joints

A computational procedure is presented for evaluating the sensitivity coefficients of the thermomechanical response of welded structures. Uncoupled thermomechanical analysis, with transient thermal analysis and quasi-static mechanical analysis, is performed. A rate independent, small deformation thermo-elasto-plastic material model with temperature-dependent material properties is adopted in the study. The temperature field is assumed to be independent of the stresses and strains. The heat transfer equations emanating from a finite element semi-discretization are integrated using an implicit backward difference scheme to generate the time history of the temperatures. The mechanical response during welding is then calculated by solving a generalized plane strain problem. First- and second-order sensitivity coefficients of the thermal and mechanical response quantities (derivatives with respect to various thermomechanical parameters) are evaluated using a direct differentiation approach in conjunction with an automatic differentiation software facility. Numerical results are presented for a double fillet conventional welding of a stiffener and a base plate made of stainless steel AL-6XN material. Time histories of the response and sensitivity coefficients, and their spatial distributions at selected times are presented.     

A dissipation-based control method for the multi-scale modelling of quasi-brittle materials

Multi-scale models based on computational homogenisation are nowadays developed for the simulation of complex material behaviour. The use of homogenisation techniques on finite-sized representative volume elements in the presence of quasi-brittle damage may lead to the presence of snap-backs in the macroscopic material response. A methodology to simulate this type of response in the multi-scale technique is proposed, based on the control of the dissipation at the mesoscopic scale. To cite this article: T.J. Massart et al., C. R. Mecanique 333 (2005).     

Mechanical homogenisation of masonry wall without mortar

Some refractory linings of metallurgical vessels consist of masonry without mortar. To describe the mechanical behaviour of these large-sized structures, it is necessary to use an equivalent material instead of a model that comprises all the bricks and joints involved. The properties of the equivalent material depend on the opening and closure mechanism of joints. In this paper, four joint states which are the combination of open/closed states of bed and head joints are identified, and the corresponding equivalent elastic properties are determined accordingly using homogenisation techniques. The transition criterion between these joint states is based on the unilateral contact conditions written in terms of macroscopic strain. The developed model is then compared to an in-plane biaxial compression test. The numerical and experimental results are in good agreement.     

Multi-scale modelling of strongly heterogeneous 3D composite structures using spatial Voronoi tessellation

3D composite materials are characterized by complex internal yarn architectures, leading to complex deformation and failure development mechanisms. Net-shaped preforms, which are originally periodic in nature, lose their periodicity when the fabric is draped, deformed on a tool, and consolidated to create geometrically complex composite components. As a result, the internal yarn architecture, which dominates the mechanical behaviour, becomes dependent on the structural geometry. Hence, predicting the mechanical behaviour of 3D composites requires an accurate representation of the yarn architecture within structural scale models. When applied to 3D composites, conventional finite element modelling techniques are limited to either homogenised properties at the structural scale, or the unit cell scale for a more detailed material property definition. Consequently, these models fail to capture the complex phenomena occurring across multiple length scales and their effects on a 3D composite’s mechanical response. Here a multi-scale modelling approach based on a 3D spatial Voronoi tessellation is proposed. The model creates an intermediate length scale suitable for homogenisation to deal with the non-periodic nature of the final material. Information is passed between the different length scales to allow for the effect of the structural geometry to be taken into account on the smaller scales. The stiffness and surface strain predictions from the proposed model have been found to be in good agreement with experimental results.The proposed modelling framework has been used to gain important insight into the behaviour of this category of materials. It has been observed that the strain and stress distributions are strongly dependent on the internal yarn architecture and consequently on the final component geometry. Even for simple coupon tests, the internal architecture and geometric effects dominate the mechanical response. Consequently, the behaviour of 3D woven composites should be considered to be a structure specific response rather than generic homogenised material properties.     

Homogenised constitutive model coupling damage and debonding for reinforced concrete structures under cyclic solicitations

A new stress resultant constitutive model for reinforced concrete plates under cyclic solicitations is presented. This model is built by the periodic homogenisation approach using the averaging method and couples damage of concrete and periodic debonding between concrete and steel rebar. In one-dimensional situations, we derive a closed-form solution of the local problem useful to verify and set up the plate problem. The one dimensional macroscopic constitutive model involves a limited number of parameters, the sensibility of which is studied. Comparison to experimental results underlines the pertinence of the model by considering internal debonding in order to properly represent the mechanical dissipation occurring during cyclic loadings on reinforced concrete panels.     

Self-consistent elastoplastic stress solutions for functionally graded material systems subjected to thermal transients

In this work, a self-consistent constitutive framework is proposed to describe the behaviour of a generic three-layered system containing a functionally graded material (FGM) layer subjected to thermal loading. Analytical and semi-analytical solutions are obtained to describe the thermo-elastic and thermo-elastoplastic behaviour of a three-layered system consisting of a metallic and a ceramic layer joined together by an FGM layer of arbitrary composition profile. Solutions for the stress distributions in a generic FGM system subjected to arbitrary temperature transient conditions are presented. The homogenisation of the local elastoplastic FGM behaviour in terms of the properties of its individual phases is performed using a self-consistent approach. In this work, power-law strain hardening behaviour is assumed for the FGM metallic phase. The stress distributions within the FGM systems are compared with accurate numerical solutions obtained from finite element analyses and good agreement is found throughout. Solutions are also given for the critical temperature transients required for the onset of plastic deformation within the three-layered systems.     

Effect of Oxidation-Induced Material Parameter Variation on the High Temperature Oxidation Behavior of Nickel

In high temperature oxidation environment, the oxidation reaction will induce variations in material parameters, such as Young's modulus, thermal expansion coefficient(CTE),coefficient of oxygen diffusion(COD), etc. The oxidation-induced material parameter variations should be considered in high temperature mechanical analysis. In this paper, high temperature oxidation behavior of an oxide film/metal substrate system was investigated through a modified phase field approach. The oxidative stress and oxidation weight gain induced by high temperature oxidation were studied. Effects of Young's modulus, COD and CTE on oxidative stress in the oxide film were studied particularly. The simulation results showed that a better agreement with the experimental results could be obtained when considering the oxidation-induced material parameter variations in the high temperature mechanical analysis of oxide film/metal substrate system. The simulation results demonstrated that oxidative stress and oxidation weight gain were more sensitive to the variation of Young's modulus than to the variations of COD and CTE.     

X-ray-diffraction approach for studies on fatigue and creep

It is well known that X-ray diffraction is one of the most powerful means for investigating the microscopic structure of crystalline materials. X-ray diffraction is advantageous when it is applied to metallic materials; it responds very sensitively to changes in the metal's crystalline structure. Another characteristic advantage of the X-ray-diffraction approach is its nondestructive nature in the measurement of crystalline-material parameters, enabling us to observe the process of mechanical phenomena of metals, such as fatigue and creep. The X-ray-diffraction patterns obtained on a deformed material include a great deal of information covering the microscopic and macroscopic characters consistent with the nature of the existing material. Residual stress measured by means of X ray is called the macroscopic-material parameter. It is evaluated by measuring the shift of the peak of a diffraction profile. The diffusiveness of the profile corresponds to the irregularity in microscopic structure of deformed crystalline material and it is noted as the submacroscopic material parameter. The X-ray-microbeam diffraction technique supplies information on the change in microscopic structure such as subgrain size, misorientation and microlattice strain. Profile analysis is another way to evaluate the microscopic-material parameters: particle size and microscopic strain. By appropriately combining these techniques in the study of mechanical behavior of materials, the parameters that control the phenomena may be extracted to facilitate discussion of their mechanism. In this lecture, X-ray-diffraction techniques to evaluate the macroscopic, submacroscopic and microscopic-material parameters are presented and the approach is demonstrated by exhibiting a case of studies on fatigue and creep of carbon steels at room and elevated temperature, where phenomena are discussed in terms of the change in the material parameters. Initiation and propagation of fatigue crack in steel at room temperature, the change in microstructure during isothermal and thermal fatigue, and also that in creep at elevated temperature under variational load are presented.     

Second-order homogenisation of functionally graded materials

The homogenisation theory for periodic composites is generalised to the case of quasi-periodic composites. In quasi-periodic composites, the unit cell does not repeat throughout the medium but gradually changes along one or more directions of periodicity (grading directions). Quasi-periodic composites are thus to functionally graded materials (FGMs) what periodic composites are to statistically uniform composite materials. Contrarily to most of the homogenisation methods applied to FGMs, the proposed second-order homogenisation theory takes explicitly into account the grading at the micro-level. The derived equivalent material happens to be a particular second gradient material in which few components of the strain gradient (second gradient of the displacement) should be taken into account in addition to the classical strains (first gradient of displacement). The second gradient theory therefore appears as the natural framework to appropriately handle functionally graded materials at the macro-level. It is worth mentioning that the presented second-order homogenisation procedure is somehow analogous to the one developed for periodic composite materials submitted to rapidly varying macroscopic strain fields as in regions of high gradients. In fact, both are a generalisation of the first-order homogenisation theory for periodic media and lead to a second gradient equivalent material. However, besides their different domains of application, they exhibit further substantial differences, which are highlighted in the paper.     

A micro-mechanical model for the homogenisation of masonry

Masonry is a composite material made of units (brick, blocks, etc.) and mortar. For periodic arrangements of the units, the homogenisation techniques represent a powerful tool for structural analysis. The main problem pending is the errors introduced in the homogenisation process when large difference in stiffness are expected for the two components. This issue is obvious in the case of non-linear analysis, where the tangent stiffness of one component or the tangent stiffness of the two components tends to zero with increasing inelastic behaviour.The paper itself does not concentrate on the issue of non-linear homogenisation. But as the accuracy of the model is assessed for an increasing ratio between the stiffness of the two components, the benefits of adopting the proposed method for non-linear analysis are demonstrated. Therefore, the proposed model represents a major step in the application of homogenisation techniques for masonry structures.The micro-mechanical model presented has been derived from the actual deformations of the basic cell and includes additional internal deformation modes, with regard to the standard two-step homogenisation procedure. These mechanisms, which result from the staggered alignment of the units in the composite, are of capital importance for the global response. For the proposed model, it is shown that, up to a stiffness ratio of one thousand, the maximum error in the calculation of the homogenised Young's moduli is lower than five percent. It is also shown that the anisotropic failure surface obtained from the homogenised model seems to represent well experimental results available in the literature.     

A micromechanically motivated material model for the thermo-viscoelastic material behaviour of rubber-like polymers

The material behaviour of rubber at the micro level is usually described by means of statistical mechanics. In particular, the Neo-Hooke model has been derived in this fashion. The micromechanical modelling can be extended to include also the breaking and reforming of chains. One possible approach at this level is the so-called transient network theory. Using certain assumptions for the chain distributions, one arrives at a continuum mechanical model of finite viscoelasticity which is based on the multiplicative decomposition of the deformation gradient. This means that the inelastic part of the deformation is regarded as an elastic isomorphism. Further, the considerations at the micro level give information about the temperature dependence of the mechanical material parameters. For instance, it can be shown easily that the shear modulus depends approximately linearly on the temperature. This fact has important consequences for thermo-mechanical coupling which have not yet been discussed in detail in the literature.     

Transient heating of opaque and semitransparent materials by radiation during processing

Analysis is presented of transient heating of opaque and semitransparent (translucent) materials by external radiation sources. Such problems arise in materials processing and manufacturing applications. Dynamic temperature distributions are calculated in a plate (slab) of material by accounting for spectral nature of the radiation source and the radiative properties of the material. Effects of radiation properties influenced by the choice of material to be heated, chemical and mechanical treatment, radiation source temperature, and convective heat transfer are considered. Differences in temperature response of opaque and semitransparent materials are examined. It is shown that the temperature distribution in a semitransparent material heated by an external radiation source is more uniform than in an opaque material for otherwise the same conditions owing to the “long range” transport of radiation. Treatment of a semitransparent material as opaque results in an unrealistic prediction of temperature distribution when the material is heated by an infrared radiation source. Received on 10 April 2000     

微振激励下黏弹性阻尼器微观链结构力学模型

减小微振动对高精密仪器至关重要,利用黏弹性阻尼器进行微振动抑制是一个新兴而又具有挑战性的课题.本文采用分子链网络模型方法分析了黏弹性材料的微观分子链结构,综合考虑材料分子链结构中的网络链和自由链对黏弹性材料力学性能的影响,提出一种基于材料微观分子链结构的微振激励下黏弹性阻尼器力学模型.模型分别采用标准线性固体模型和Maxwell模型来描述网络链和自由链中单个链的力学性能,并分别采用8链网络模型和3链网络模型考虑两种类型分子链的综合效应,引入温频等效原理描述温度对微振激励下黏弹性阻尼器力学性能的影响.该模型能够描述温度和频率对黏弹性阻尼器动态力学性能的影响,并能够反映黏弹性材料的微观结构与材料力学性能的关系.为验证所提模型的有效性及考察黏弹性阻尼器在微振激励下的耗能能力和动态力学性能,在微振条件下对黏弹性阻尼器进行了动态力学性能试验.研究结果表明黏弹性阻尼器具有较好的微振耗能能力,其动态力学性能受温度和频率影响较大,所提的力学模型能够精确地描述微振激励下黏弹性阻尼器动态力学性能随温度和频率的变化关系.