Homogenization process of stratified masonry

Carbone, Vincenzo Ilario; Codegone, Marco

doi:10.1016/j.mcm.2004.03.009

Cited by 6 publications

(5 citation statements)

References 6 publications

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“…Next, stress-strain analysis is performed on the macrostructure using the homogenized elasticity tensor E M(d) ijkl as the elastic tensor of each domain, and the local stress is obtained from the characteristic strain 𝜒 kl (d) m,n of the microstructure and the strain u M(d) k,l of the macrostructure based on Equation (6). The local stress is obtained from the elemental strains of the macrostructure and microstructure, so it is derived as the product of the number of elements in the macrostructure and microstructure.…”

Section: Optimization System Flowmentioning

confidence: 99%

“…5 Carbone and Codegone incorporated the homogenization method into problems arising in civil engineering, and obtained the mechanical properties of a periodic masonry structure composed of bricks and mortar using the finite element method. 6 Zhou et al proposed a stochastic homogenization method that combines the homogenization method with a stochastic finite element method to predict the effective elastic properties of fiber composites. 7 Regarding on strength problem, Takano et al combined the homogenization method with anisotropic damage studies to evaluate the strength of fiber bundles focusing on failure in a woven structure.…”

Section: Introductionmentioning

confidence: 99%

“…Terada et al assumed an anisotropic hyperelastic constitutive law as a macro‐material model for fiber‐reinforced composites with periodic microstructures, and also proposed a method to identify the material parameters of the assumed macrostructure through analysis of the microstructure by applying numerical material experiments based on the homogenization method 5 . Carbone and Codegone incorporated the homogenization method into problems arising in civil engineering, and obtained the mechanical properties of a periodic masonry structure composed of bricks and mortar using the finite element method 6 . Zhou et al proposed a stochastic homogenization method that combines the homogenization method with a stochastic finite element method to predict the effective elastic properties of fiber composites 7 .…”

Section: Introductionmentioning

confidence: 99%

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Shape optimization method for strength design problem of microstructures in a multiscale structure

TORISAKI

Shimoda

Ali

2022

Numerical Meth Engineering

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In this paper, we propose a solution to a shape optimization problem for the strength design of periodic microstructures in multiscale structures. Two maximum stress minimization problems are addressed: minimization of maximum microstructural stress and minimization of maximum macrostructural stress.The homogenization method is used to bridge the macrostructure and the microstructure and to calculate local microstructural stress. By replacing the maximum stress value with a Kreisselmeier-Steinhauser function, the difficulty of nondifferentiability of maximum stress is avoided. Each strength design problem is formulated as a distributed parameter optimization problem subject to an area constraint including the whole microstructure. The shape gradient functions for both problems are derived using Lagrange's undetermined multiplier method, the material derivative method, and the adjoint variable method. The H 1 gradient method is used to determine the unit cell shapes of the microstructure, while reducing the objective function and maintaining smooth design boundaries. In the numerical examples, the optimal shapes obtained for minimization of the maximum local stress of the microstructure and the macrostructure are compared and discussed. The results confirm the effectiveness of the microstructure shape optimization method for the two strength design problems of multiscale structures.

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Section: Optimization System Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shape optimization method for strength design problem of microstructures in a multiscale structure

TORISAKI

Shimoda

Ali

2022

Numerical Meth Engineering

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“…Los datos obtenidos en las pruebas aplicadas a los morteros se recogen en la Tabla 2. Por norma general se asume que en la mampostería, ladrillos y morteros exhiben muy distintas propiedades, dificultando la identificación de una ley única capaz de proveer una descripción global del comportamiento mecánico del conjunto, lo que a su vez hace necesario apelar a los principios de la teoría de la homogenización de la mampostería expuesta por varios autores [1], [3] y [4]. En esta investigación, a partir de los resultados experimentales y de acuerdo con las Ecuaciones (1) y (2), correspondiente a las Ec.…”

Section: Caracterización De La Mamposteríaunclassified

Análisis de un edificio histórico usando MEF: El puente La Libertad, en Buga - Valle del Cauca (1874)

Díaz

López

Méndez

2007

Cien.Ing.Neogranadina

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RESUMENEste documento presenta parte de los resultados de un proyecto de investigación mucho más amplio que ha reconocido aspectos históricos y técnicos propios de un conjunto de 34 puentes históricos de arco de ladrillo, de los cuales aun existen 20, todos con característi-cas geométricas diversas y dimensiones singulares. Se expone el proceso de modelamiento numérico mediante el método de elementos finitos (MEF) adelantado en uno de ellos y se presentan conclusiones que se pueden extender a la casi totalidad de los casos estudiados con el fin de ofrecer nuevas alternativas de análisis a los profesionales interesados en la rehabilitación y conservación del patrimonio arquitectónico e ingenieril colombiano.PALABRAS CLAVE: puentes de arco de ladrillo, análisis estructural, método de elementos finitos. ABSTRACTThis document presents partial results of a much broader research project that has recognized historical and technical aspects pertaining to a set of 34 historic brick arch bridges, 20 of which still exist, all with diverse geometric characteristics and singular dimensions. The methodological process is exposed as carried out with one of them and conclusions are presented, which can be extended to almost the totality of the cases studied for the purpose of offering new analysis alternatives to professionals interested in the rehabilitation and conservation of the Colombian architectural and engineering patrimony.

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“…The first method involves macroscopic models, in which the wall is assumed to be a single structural element characterized by a non linear response when it is exposed to shear forces [1,2,3,4,5,6,7,37]. These models, which are generally based on the use of homogenization techniques, usually take the properties of the materials and the bonding between the various components into account [24,25,26,27,28,29,30,31,32,33,34,35].…”

Section: Introductionmentioning

confidence: 99%

Homogenization methods for interface modeling in damaged masonry

Rekik

Lebon²

2012

Advances in Engineering Software

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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

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Homogenization process of stratified masonry

Cited by 6 publications

References 6 publications

Shape optimization method for strength design problem of microstructures in a multiscale structure

Shape optimization method for strength design problem of microstructures in a multiscale structure

Análisis de un edificio histórico usando MEF: El puente La Libertad, en Buga - Valle del Cauca (1874)

Homogenization methods for interface modeling in damaged masonry

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