A systematic methodology for an accurate evaluation of various existing linearization procedures sustaining mean fields theories for nonlinear composites is proposed and applied to recent homogenization methods. It relies on the analysis of a periodic composite for which an exact resolution of both the original nonlinear homogenization problem and the linear homogenization problems associated with the chosen linear comparison composite (LCC) with an identical microstructure is possible. The effects of the sole linearization scheme can then be evaluated without ambiguity. This methodology is applied to three different two-phase materials in which the constitutive behavior of at least one constituent is nonlinear elastic (or viscoplastic): a reinforced composite, a material in which both phases are nonlinear and a porous material. Comparisons performed on these three materials between the considered homogenization schemes and the reference solution bear out the relevance and the performances of the modified second-order procedure introduced by Ponte Castañ eda in terms of prediction of the effective responses. However, under the assumption that the field statistics (first and second moments) are given by the local fields in the LCC, all the recent nonlinear homogenization procedures still fail to provide an accurate enough estimate of the strain statistics, especially for composites with high contrast.
International audienceThe aim of the present study was to reproduce damage in masonry by combining structural analysis and homogenization methods. In the case of a masonry structure composed of bricks and mortar, a third material is assumed to exist, which is a mixture of the two materials sandwiched between the other two. This new layer has a small thickness, a low stiffness and a given damage ratio. The mechanical problem set by this masonry, which was initially a 3-D problem, is solved numerically in 2-D terms using finite element methods and modeling the three materials: brick, mortar and the interface material defined above. The properties of the third material are obtained by performing the following three steps: (i) Firstly an exact homogenization of a brick/mortar laminate defining a first homogeneous equivalent medium (HEM-1) is performed. (ii) Secondly, we assume the HEM-1 to be damaged and apply the Kachanov model to assess the global behavior of the damaged HEM-1, thus defining a second equivalent homogeneous medium denoted HEM-2. (iii) Thirdly, an asymptotic analysis is performed to model HEM-2 as an interface or a joint. The properties of this joint are deduced from those of the HEM-2 material. This interface is modeled numerically with connector finite elements. This method is applied to two cases: a triplet of full bricks and a triplet of hollow bricks both subjected to shear loading. The numerical results obtained are compared with experimental data available in the literature
To support optimisation of refractory masonry structures compressibility of dry joints of magnesia-carbon and magnesia-chromite bricks have been investigated. Laboratory scale tests and finite element modelling have been performed. Measurements done in wide temperature range have shown that the exponential form of the joint closure curve results from gradual closure of initially non parallel surfaces. The stress needed to close the joint was found to be proportional to the material stiffness. Temperature influences the joint closure by changing the stiffness of material and by reducing the initial joint gap due to thermal expansion. IntroductionRefractory ceramic linings of high temperature furnaces are often built with bricks. Brick chemical composition and geometry are selected regarding the service conditions and the lining structure [1]. Due to the conditions of constrained thermal expansion high compressive stresses often develop in the bricks [2]. In many furnaces, including the blast furnace and the converter of the steel industry, bricks are laid on a dry joint, without usage of mortar. Most investigations on the mechanics of masonry consider civil structures with mortared joints [3][4][5]. Behaviour of the dry joints, especially in the refractory masonry, is less investigated. It is known that under compression the stiffness of the refractory lining will decrease with increasing amount of joints [6]. At room temperature the dry joint closure has been measured for alumino-silicate refractory bricks. Optical technique was used for the purpose. The ability of the dry joint to reduce compressive stresses was attributed to imperfect initial contact due to the roughness of the brick faces [7]. The quantitative knowledge of joint effects is an essential design parameter. As an example one can regard the superposition of the stress reducing effect of the joint and of expansion release inserts. The latter are introduced in form of card-board plates in several joints of the masonry wall to allow free expansion when the card-board burns up [2]. If the combined effect of the joints and the inserts is too high the lining is not tight enough. In the cyclic operation combining regular heating and cooling, and in some cases featuring rotational movement, loose lining can lose its stability and collapse. On another hand, too tight lining may fail under high compressive stresses. This paper investigates the compressive closure of dry joints in two classes of refractory bricks -magnesia carbon and magnesia chromite bricks. Regarding the service conditions of the bricks the measurements were performed in wide temperature range. The process of joint closure was measured indirectly by compressing samples with and without joints. At room temperature, also direct optical measurements were performed. FEM computer analysis was used to interpret the measurement results. The general aim of the investigation was to obtain data on the compressive joint closure behaviour to get a better insight into the masonry stress state a...
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