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1.
A simplified kinematic procedure at a cell level is proposed to obtain in-plane elastic moduli and macroscopic masonry strength domains in the case of herringbone masonry. The model is constituted by two central bricks interacting with their neighbors by means of either elastic or rigid-plastic interfaces with friction, representing mortar joints. The herringbone pattern is geometrically described and the internal law of composition of the periodic cell is defined.A sub-class of possible elementary deformations is a-priori chosen to describe joints cracking under in-plane loads. Suitable internal macroscopic actions are applied on the Representative Element of Volume (REV) and the power expended within the 3D bricks assemblage is equated to that expended in the macroscopic 2D Cauchy continuum. The elastic and limit analysis problem at a cell level are solved by means of a quadratic and linear programming approach, respectively.To assess elastic results, a standard FEM homogenization is also performed and a sensitivity analysis regarding two different orientations of the pattern, the thickness of the mortar joints and the ratio between block and mortar Young moduli is conducted. In this way, the reliability of the numerical model is critically evaluated under service loads.When dealing with the limit analysis approach, several computations are performed investigating the role played by (1) the direction of the load with respect to herringbone bond orientation, (2) masonry texture and (3) mechanical properties adopted for joints.At a structural level, a FE homogenized limit analysis is performed on a masonry dome built in herringbone bond. In order to assess limit analysis results, additional non-linear FE analyses are performed, including a full 3D numerical expensive heterogeneous approach and models where masonry is substituted with an equivalent macroscopic material with orthotropic behavior and possible softening. Reliable predictions of collapse loads and failure mechanisms are obtained, meaning that the approach proposed may be used by practitioners for a fast evaluation of the effectiveness of herringbone bond orientation. 相似文献
2.
A mechanistic model with rigid elements and interfaces suitable for the non-linear dynamic analysis of full scale 3D masonry buildings is presented. The model relies into two steps: in the first step, a simplified homogenization is performed at the meso-scale to deduce the mechanical properties of a macroscopic material, to be used in structural applications; the second step relies into the implementation of a Rigid Body and Spring Model (RBSM) constituted by rigid elements linked with homogenized interfaces. In the homogenization step, a running bond elementary cell is discretized with 24 three-node plane-stress elastic triangular elements and non-linear interfaces representing mortar joints. It is shown how the mechanical problem in the unit cell is characterized by few displacement variables and how homogenized stress–strain curves can be evaluated by means of a semi-analytical approach. The second step relies on the implementation of the homogenized curves into a RBSM, where an entire masonry structure can be analyzed in the non-linear dynamic range through a discretization with rigid elements and inelastic interfaces. Non-linear structural analyses are conducted on a church façade interconnected with a portion of the perpendicular walls and on a small masonry building, for which experimental and numerical data are available in the literature, in order to show how quite reliable results may be obtained with a limited computational effort. 相似文献
3.
Approximate expressions for the macroscopic out-of-plane elastic coefficients of brick masonry with a regular pattern are derived in closed form using a homogenization approach for periodic media. Following an approach similar to the Method of Cells for fiber reinforced composites, a (piecewise-)differentiable expression depending on very a limited number of degrees of freedom and fulfilling suitable periodicity conditions is proposed for the microscopic transverse displacement field over any Representative Volume Element (RVE). Some of the equilibrium conditions at the interfaces between bricks and mortar joints are also fulfilled. By averaging the moment and curvature fields over the RVE, the macroscopic bending stiffness coefficients can be explicitly obtained. Using the FE solution of a masonry panel subjected to elementary load conditions as a benchmark, the proposed approach is found to accurately match the numerically obtained stiffness coefficients, for masonry elements of different geometry and different mechanical properties. In several instances, the proposed expressions agree with the numerical predictions better than other analytical expressions available in the literature. 相似文献
4.
A 3D model for the evaluation of the non-linear behavior of masonry double curvature structures is presented. In the model, the heterogeneous assemblage of blocks is substituted with a macroscopically equivalent homogeneous non-linear material. At the meso-scale, a curved running bond representative element of volume (REV) constituted by a central block interconnected with its six neighbors is discretized through of a few six-noded rigid wedge elements and rectangular interfaces. Non linearity is concentrated exclusively on joints reduced to interface, exhibiting a frictional behavior with limited tensile and compressive strength with softening. The macroscopic homogenous masonry behavior is then evaluated on the REV imposing separately increasing internal actions (in-plane membrane actions, meridian and parallel bending, torsion and out-of-plane shear). This simplified approach allows to estimate heuristically the macroscopic stress–strain behavior of masonry at the meso-scale. The non-linear behavior so obtained is then implemented at a structural level in a novel FE non-linear code, relying on an assemblage of rigid infinitely resistant six-noded wedge elements and non-linear interfaces, exhibiting deterioration of the mechanical properties.Several numerical examples are analyzed, consisting of two different typologies of masonry arches (a parabolic vault and an arch in a so-called “skew” disposition), a ribbed cross vault, a hemispherical dome and a cloister vault. To fully assess numerical results, additional non-linear FE analyses are presented. In particular, a simplified model is proposed, which relies in performing at a structural level a preliminary limit analysis – which allows to identify the failure mechanism – and subsequently in modeling masonry through elastic elements and non-linear interfaces placed only in correspondence or near the failure mechanism provided by limit analysis. Simulations performed through an equivalent macroscopic material with orthotropic behavior and possible softening are also presented, along with existing experimental evidences (where available), in order to have a full insight into the capabilities and limitations of the approach proposed. 相似文献
5.
The aim of this paper is to study non-periodic masonries – typical of historical buildings – by means of a perturbation approach and to evaluate the effect of a random perturbation on the elastic response of a periodic masonry wall. The random masonry is obtained starting from a periodic running bond pattern. A random perturbation on the horizontal positions of the vertical interfaces between the blocks which form the masonry wall is introduced. In this way, the height of the blocks is uniform, while their width in the horizontal direction is random. The perturbation is limited such as each block has still exactly 6 neighboring blocks. In a first discrete model, the blocks are modeled as rigid bodies connected by elastic interfaces (mortar thin joints). In other words, masonry is seen as a “skeleton” in which the interactions between the rigid blocks are represented by forces and moments which depend on their relative displacements and rotations. A second continuous model is based on the homogenization of the discrete model. Explicit upper and lower bounds on the effective elastic moduli of the homogenized continuous model are obtained and compared to the well-known effective elastic moduli of the regular periodic masonry. It is found that the effective moduli are not very sensitive to the random perturbation (less than 10%). At the end, the Monte Carlo simulation method is used to compare the discrete random model and the continuous model at the structural level (a panel undergoing in plane actions). The randomness of the geometry requires the generation of several samples of size L of the discrete masonry. For a sample of size L, the structural discrete problem is solved using the same numerical procedure adopted in [Cecchi, A., Sab, K., 2004. A comparison between a 3D discrete model and two homogenized plate models for periodic elastic brickwork, International Journal of Solids Structures 41 (9–10), 2259–2276] and the average solution over the samples gives an estimation which depends on L. As L increases, an asymptotic limit is reached. One issue is to find the minimum size for L and to compare the asymptotic average solution to the one obtained from the continuous homogenized model. 相似文献
6.
This study presents a two-scale model to describe the out-of-plane masonry response. One-dimensional (1D) structural elements, like masonry columns or strips of long wall characterized by the periodic repetition of bricks and mortar arranged in stack bond, are considered. A damage-friction plasticity law is adopted to model the mortar joint constitutive response, while the bricks are assumed as linear elastic. A 1D beam formulation is introduced at both the structural and micromechanical scale, linking the two levels by means of a kinematic map. This expresses the microscopic beam strains in the masonry unit cell (UC) as function of the macroscopic generalized strains. The kinematic field in the UC is completed by adding an unknown periodic fluctuation term. A nonlinear homogenization procedure is developed, proposing a semi-analytical solution for the micromechanical problem, based on the fiber discretization of the mortar joints. A force-based beam-column finite element procedure is adopted at the structural scale and the solution algorithm for the element state determination is illustrated in details. Some numerical applications, showing the UC constitutive response and the behavior of masonry structural elements, are finally presented. 相似文献
7.
Gabriele Milani Paulo B. Lourenço Antonio Tralli 《International Journal of Solids and Structures》2009,46(22-23):4133-4149
A simple rigid-plastic homogenization model for the analysis of masonry structures subjected to out-of-plane impact loads is presented. The objective is to propose a model characterized by a few material parameters, numerically inexpensive and very stable. Bricks and mortar joints are assumed rigid perfectly plastic and obeying an associated flow rule. In order to take into account the effect of brickwork texture, out-of-plane anisotropic masonry failure surfaces are obtained by means of a limit analysis approach, in which the unit cell is sub-divided into a fixed number of sub-domains and layers along the thickness. A polynomial representation of micro-stress tensor components is utilized inside each sub-domain, assuring both stress tensor admissibility on a regular grid of points and continuity of the stress vector at the interfaces between contiguous sub-domains. Limited strength (frictional failure with compressive cap and tension cut-off) of brick-mortar interfaces is also considered in the model, thus allowing the reproduction of elementary cell failures due to the possible insufficient resistance of the bond between units and joints.Triangular Kirchhoff-Love elements with linear interpolation of the displacement field and constant moment within each element are used at a structural level. In this framework, a simple quadratic programming problem is obtained to analyze entire walls subjected to impacts.In order to test the capabilities of the approach proposed, two examples of technical interest are discussed, namely a running bond masonry wall constrained at three edges and subjected to a point impact load and a masonry square plate constrained at four edges and subjected to a distributed dynamic pressure simulating an air-blast. Only for the first example, numerical and experimental data are available, whereas for the second example insufficient information is at disposal from the literature. Comparisons with standard elastic–plastic procedures conducted by means of commercial FE codes are also provided. Despite the obvious approximations and limitations connected to the utilization of a rigid-plastic model for masonry, the approach proposed seems able to provide results in agreement with alternative expensive numerical elasto-plastic approaches, but requiring only negligible processing time. Therefore, the proposed simple tool can be used (in addition to more sophisticated but expensive non-linear procedures) by practitioners to have a fast estimation of masonry behavior subjected to impact. 相似文献
8.
Antonella Cecchi Antonio Tralli 《International Journal of Solids and Structures》2012,49(13):1485-1496
A linear viscous model for evaluating the stresses and strains produced in masonry structures over time is presented. The model is based on rigorous homogenization procedures and the following two assumptions: that the structure is composed of either rigid or elastic blocks, and that the mortar is viscoelastic. The hypothesis of rigid block is particularly suitable for historical masonry, in which stone blocks may be assumed as rigid bodies, while the hypothesis of elastic blocks may be assumed for newly constructed brickwork structures. The hypothesis of viscoelastic mortar is based on the observation that non-linear phenomena may be concentrated in mortar joints. Under these assumptions, constitutive homogenized viscous functions are obtained in an analytical form.Some meaningful cases are discussed: masonry columns subject to minor and major eccentricity, and a masonry panel subject to both horizontal and vertical loads. The major eccentricity case is analysed taking into account both the effect of viscosity and the no-tension hypothesis, whereas the bi-dimensional loading case is analysed to verify the sensitivity of masonry behaviour to viscous function. In the masonry wall considered, the principal stresses are both of compression, and the no-tension assumption may therefore be discounted. 相似文献
9.
Two-wythes masonry walls arranged in English bond texture were often used in the past as bearing panels in seismic area. On the other hand, earthquake surveys have demonstrated that masonry strength under horizontal actions is usually insufficient, causing premature collapses of masonry buildings, often ascribed to out-of-plane actions. Furthermore, many codes of practice impose for new brickwork walls a minimal slenderness, which for instance is fixed by the Italian O.P.C.M. 3431 equal to 12 for artificial bricks and 10 for natural blocks masonry.For the above reasons, the analysis at failure of English bond brickwork walls under out-of-plane actions is a topic that deserves consideration, despite the fact that almost the totality of the studies of masonry at failure is devoted to running bond arrangements. Furthermore, it must be noted that an approach based on the analysis of running bond texture – in comparison with English bond pattern – is not suitable for the investigation of the behavior of bearing panels.In this framework, in the present paper, a Reissner–Mindlin kinematic limit analysis approach is presented for the derivation of the macroscopic failure surfaces of two-wythes masonry arranged in English bond texture. In particular, the behavior of a 3D system constituted by infinitely resistant bricks connected by joints reduced to interfaces with frictional behavior and limited tensile/compressive strength is identified with a 2D Reissner–Mindlin plate. In this way, assuming both an associated flow rule for the constituent materials and a finite subclass of possible deformation modes, an upper bound approximation of macroscopic English bond masonry failure surfaces is obtained as a function of macroscopic bending moments, torsion and shear forces.Several examples of technical relevance are treated both at a cell level and at a structural level, addressing the differences in terms of collapse loads and failure surfaces due to different textures and constituent laws for joints. Finally, two meaningful structural examples consisting of a panel in cylindrical flexion and a masonry slab constrained at three edges and out-of-plane loaded are discussed. A detailed comparison in terms of deformed shapes at collapse and failure loads between a 2D FE Reissner–Mindlin limit analysis approach and a full 3D heterogeneous FE model shows the reliability of the results obtained using the kinematic identification approach proposed. 相似文献
10.
《International Journal of Solids and Structures》2007,44(18-19):6055-6079
This paper describes a new procedure for the homogenization of orthotropic 3D periodic plates. The theory of Caillerie [Caillerie, D., 1984. Thin elastic and periodic plates. Math. Method Appl. Sci., 6, 159–191.] – which leads to a homogeneous Love–Kirchhoff model – is extended in order to take into account the shear effects for thick plates. A homogenized Reissner–Mindlin plate model is proposed. Hence, the determination of the shear constants requires the resolution of an auxiliary 3D boundary value problem on the unit cell that generates the periodic plate. This homogenization procedure is then applied to periodic brickwork panels.A Love–Kirchhoff plate model for linear elastic periodic brickwork has been already proposed by Cecchi and Sab [Cecchi, A., Sab, K., 2002b. Out-of-plane model for heterogeneous periodic materials: the case of masonry. Eur. J. Mech. A-Solids 21, 249–268 ; Cecchi, A., Sab, K., 2006. Corrigendum to A comparison between a 3D discrete model and two homogenised plate models for periodic elastic brickwork [Int. J. Solids Struct., vol. 41/9–10, pp. 2259–2276], Int. J. Solids Struct., vol. 43/2, pp. 390–392.]. The identification of a Reissner–Mindlin homogenized plate model for infinitely rigid blocks connected by elastic interfaces (the mortar thin joints) has been also developed by the authors Cecchi and Sab [Cecchi A., Sab K., 2004. A comparison between a 3D discrete model and two homogenised plate models for periodic elastic brickwork. Int. J. Solids Struct. 41/9–10, 2259–2276.]. In that case, the identification between the 3D block discrete model and the 2D plate model is based on an identification at the order 1 in the rigid body displacement and at the order 0 in the rigid body rotation.In the present paper, the new identification procedure is implemented taking into account the shear effect when the blocks are deformable bodies. It is proved that the proposed procedure is consistent with the one already used by the authors for rigid blocks. Besides, an analytical approximation for the homogenized shear constants is derived. A finite elements model is then used to evaluate the exact shear homogenized constants and to compare them with the approximated one. Excellent agreement is found. Finally, a structural experimentation is carried out in the case of masonry panel under cylindrical bending conditions. Here, the full 3D finite elements heterogeneous model is compared to the corresponding 2D Reissner–Mindlin and Love–Kirchhoff plate models so as to study the discrepancy between these three models as a function of the length-to-thickness ratio (slenderness) of the panel. It is shown that the proposed Reissner–Mindlin model best fits with the finite elements model. 相似文献
11.
《International Journal of Solids and Structures》2007,44(5):1438-1460
Earthquake surveys have demonstrated that the lack of out-of-plane strength is a primary cause of failure in many traditional forms of masonry. Moreover, bearing walls are relatively thick and, as a matter of fact, many codes of practice impose a minimal slenderness for them, as for instance the recent Italian O.P.C.M. 3431 [2005. Ulteriori modifiche ed integrazioni all’OPCM 3274/03 (in Italian) and O.P.C.M. 3274, 20/03/2003, Primi elementi in materia di criteri generali per la classificazione sismica del territorio nazionale e di normative tecniche per le costruzioni in zona sismica (in Italian)], in which the upper bound slenderness is fixed respectively equal to 12 for artificial bricks and 10 for natural blocks masonry. In this context, a formulation at failure for regular assemblages of bricks based both on homogenization and Reissner–Mindlin theory seems particularly attractive. In this paper a kinematic limit analysis approach under the hypotheses of the thick plate theory is developed for the derivation of the macroscopic failure surfaces of masonry out-of-plane loaded. The behavior of a 3D system of blocks connected by interfaces is identified with a 2D Reissner–Mindlin plate. Infinitely resistant blocks connected by interfaces (joints) with a Mohr–Coulomb failure criterion with tension cut-off and compressive cap are considered. Finally, an associated flow rule for joints is adopted. In this way, the macroscopic masonry failure surface is obtained as a function of the macroscopic bending moments, torsional moments and shear forces by means of a linear programming problem in which the internal power dissipated is minimized, once that a subclass of possible deformation modes is a priori chosen. Several examples of technical relevance are presented and comparisons with previously developed Kirchhoff–Love static [Milani, G., Lourenço, P.B., Tralli, A., 2006b. A homogenization approach for the limit analysis of out-of-plane loaded masonry walls. J. Struct. Eng. ASCE (in press)] and kinematic [Sab, K., 2003.Yield design of thin periodic plates by a homogenisation technique and an application to masonry walls. C.R. Mech. 331, 641–646] failure surfaces are provided. Finally, two meaningful structural examples are reported, the first concerning a masonry wall under cylindrical flexion, the second consisting of a rectangular plate with a central opening out-of-plane loaded. For both cases, the influence of the shear strength on the collapse load is estimated. 相似文献
12.
Elio Sacco 《European Journal of Mechanics - A/Solids》2009,28(2):209-222
The present paper deals with the problem of the determination of the in-plane behavior of masonry material. The masonry is considered as a composite material composed by a regular distribution of blocks connected by horizontal and vertical mortar joints. The overall constitutive relationships of the regular masonry are derived by a rational micromechanical and homogenization procedure. Linear elastic constitutive relationship is considered for the blocks, while a new special nonlinear constitutive law is proposed for the mortar joints. In particular, a mortar constitutive law, which accounts for the coupling of the damage and friction phenomena occurring during the loading history, is proposed; the developed model is based on an original micromechanical analysis of the damage process of the mortar joint. Then, an effective nonlinear homogenization procedure, representing the main novelty of the paper, is proposed; it is based on the transformation field analysis, using the technique of the superposition of the effects and the finite element method. The presented methodology is implemented in a numerical code. Finally, numerical applications are performed in order to assess the performances of the proposed procedure in reproducing the mechanical behavior of masonry material. 相似文献
13.
Daniela Addessi Elio Sacco Achille Paolone 《European Journal of Mechanics - A/Solids》2010,29(4):724-737
The paper deals with the problem of the determination of the in-plane behavior of periodic masonry material. The macromechanical equivalent Cosserat medium, which naturally accounts for the absolute size of the constituents, is derived by a rational homogenization procedure based on the Transformation Field Analysis. The micromechanical analysis is developed considering a Cauchy model for masonry components. In particular, a linear elastic constitutive relationship is considered for the blocks, while a nonlinear constitutive law is adopted for the mortar joints, accounting for the damage and friction phenomena occurring during the loading history. Some numerical applications are performed on a Representative Volume Element characterized by a selected commonly used texture, without performing at this stage structural analyses. A comparison between the results obtained adopting the proposed procedure and a nonlinear micromechanical Finite Element Analysis is presented. Moreover, the substantial differences in the nonlinear behavior of the homogenized Cosserat material model with respect to the classical Cauchy one, are illustrated. 相似文献
14.
《European Journal of Mechanics - A/Solids》2008,27(6):1037-1059
The dynamic behavior of masonry walls strengthened with composite materials and subjected to dynamic out-of-plane loading is analytically investigated. The analytical model derived in the paper focuses on one-way action through the height of the wall and it is based on dynamic equilibrium and the compatibility conditions between the structural components (masonry units, mortar joints, FRP reinforcement, and adhesive layers). The cracking and the nonlinear and dissipative behavior of the mortar material, the breathing of cracks, the rocking phenomenon, the development of arching forces, the interaction between the existing wall and the composite system, and the formation of debonded zones near the cracked mortar joints are considered in the nonlinear dynamic analysis. A numerical study that examines the capabilities of the model, quantifies the response of the strengthened wall to dynamic loads such as free and forced vibrations and seismic base excitation, and compares it to the response of the unstrengthened wall is presented. A summary and conclusions close the paper. 相似文献
15.
A multi-scale model for the structural analysis of the in-plane response of masonry panels, characterized by periodic arrangement of bricks and mortar, is presented. The model is based on the use of two scales: at the macroscopic level the Cosserat micropolar continuum is adopted, while at the microscopic scale the classical Cauchy medium is employed. A nonlinear constitutive law is introduced at the microscopic level, which includes damage, friction, crushing and unilateral contact effects for the mortar joints. The nonlinear homogenization is performed employing the Transformation Field Analysis (TFA) technique, properly extended to the macroscopic Cosserat continuum. A numerical procedure is developed and implemented in a Finite Element (FE) code in order to analyze some interesting structural problems. In particular, four numerical applications are presented: the first one analyzes the response of the masonry Representative Volume Element (RVE) subjected to a cyclic loading history; in the other three applications, a comparison between the numerically evaluated response and the micromechanical or experimental one is performed for some masonry panels. 相似文献
16.
Karam Sab 《Comptes Rendus Mecanique》2003,331(9):641-646
A homogenization method for determining overall yield strength properties of thin periodic plates from their local strength properties is proposed within the framework of the yield design theory. The proposed method is applied to the determination of the in-plane and out of plane strength criterion for masonry described as a regular assemblage of infinitely resistant bricks separated by Coulomb interfaces. To cite this article: K. Sab, C. R. Mecanique 331 (2003). 相似文献
17.
T.M.H. Nguyen E. Blond A. Gasser T. Prietl 《European Journal of Mechanics - A/Solids》2009,28(3):535-544
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. 相似文献
18.
19.
A macroscopic model is presented aimed at assessing the macroscopic elastic behaviour of materials reinforced by periodically distributed flexible membranes. According to this model, called multiphase model, the reinforced material is described not as a single homogenized continuum as in the classical homogenization approach, but as the superposition of two mutually interacting continuous media, namely the matrix phase and the reinforcement phase. It is shown in particular how such a model allows to capture both scale and boundary effects, which cannot be accounted for in a classical homogenization procedure. 相似文献
20.
Ravi K. Burla Ashok V. Kumar Bhavani V. Sankar 《International Journal of Solids and Structures》2009,46(11-12):2514-2526
A method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented. This approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite. Implicit boundary method is used to ensure that interface conditions are satisfied at the material boundaries. In this method, solution structures for test and trial functions are constructed using approximate step functions such that the interface conditions are satisfied, even if there are no nodes on the material interface boundary. Since a structured grid does not conform to the geometry of the analysis domain, the geometry of the microstructure is defined independently using equations of the interface boundary curves/surfaces. Structured grids that overlap the geometry are easy to generate, and the elements in the grid are regular shaped and undistorted. A numerical example is presented to demonstrate that the proposed solution structure accurately models the solution across material interface, and convergence analysis is performed to show that the method converges as the grid density is increased. Fiber reinforced microstructures are analyzed to compute the effective elastic properties using both 2D and 3D models to show that the results match closely with the ones available in the literature. 相似文献