Kinematic FE limit analysis homogenization model for masonry walls reinforced with continuous FRP grids

A homogenization model for periodic masonry structures reinforced with continuous FRP grids is presented. Starting from the observation that a continuous grid preserves the periodicity of the internal masonry layer, rigid-plastic homogenization is applied directly on a multi-layer heterogeneous representative element of volume (REV) constituted by bricks, finite thickness mortar joints and external FRP grids. In particular, reinforced masonry homogenized failure surfaces are obtained by means of a compatible identification procedure, where each brick is supposed interacting with its six neighbors by means of finite thickness mortar joints and the FRP grid is applied on the external surfaces of the REV. In the framework of the kinematic theorem of limit analysis, a simple constrained minimization problem is obtained on the unit cell, suitable to estimate – with a very limited computational effort – reinforced masonry homogenized failure surfaces.A FE strategy is adopted at a cell level, modeling joints and bricks with six-noded wedge shaped elements and the FRP grid through rigid infinitely resistant truss elements connected node by node with bricks and mortar. A possible jump of velocities is assumed at the interfaces between contiguous wedge and truss elements, where plastic dissipation occurs. For mortar and bricks interfaces, a frictional behavior with possible limited tensile and compressive strength is assumed, whereas for FRP bars some formulas available in the literature are adopted to reproduce the delamination of the truss from the support.Two meaningful structural examples are considered to show the capabilities of the procedure proposed, namely a reinforced masonry deep beam (0°/90° continuous reinforcement) and a masonry beam in simple flexion for which experimental data are available. Good agreement is found between present model and alternative numerical approaches.     

Numerical simulation of the failure process of unreinforced masonry walls due to concentrated static and dynamic loading

Finite element analyses of brick masonry subjected to in-plane concentrated static and dynamic loads are carried out to study crack initiation and propagation during the failure process of unreinforced masonry walls. The numerical model is firstly validated by the experimental tests by using the same materials parameters and loading conditions. Then, the static and dynamic concentrated loads are applied to the mortar joints and brick, respectively, and numerical simulations are used to compare the fracture characteristics for these loads. In addition, a comparison of fracture mechanisms for the concentrated loads on the mortar joint and brick is also given. Finally, the effect of dynamic pressure (P_max) on the failure mechanism of brick masonry is considered.     

Experimental and Theoretical Investigation on Masonry after High Temperature Exposure

The results of experimental investigation on the mechanical properties of clay brick masonry after high temperature exposition are here presented. The adopted physical model of masonry means to represent both new and old load bearing walls, so to get useful and applicable results. Uniaxial and diagonal compressive tests were carried on masonry samples exposed to 300 and 600°C. Samples of the component materials were tested in compression as well, and the elastic moduli of bricks and mortar were also measured. The results allow to evaluate the levels of residual strength and stiffness of all tested materials after exposure to high temperatures. Finally, property-temperature laws of mechanical decay for masonry, brick and mortar after high temperature exposition are here proposed and discussed.     

Limit states for brick masonry based on homogenization approach

In this paper, a procedure is developed for assessing the strength of brick masonry based on homogenization theory. The approach invokes a lower bound analysis whereby plastically admissible stress fields are constructed in the constituents involved, subject to periodic boundary conditions and static equilibrium requirements. The critical load is obtained by solving a constrained optimization problem. The analysis employs a set of specific loading histories such as axial tension, pure shear and biaxial tension–compression at different orientations of bed joints. The performance of this approach is verified against numerical solutions based on finite element analysis. In the second part of this paper, a methodology is outlined for identification of a macroscopic failure criterion that incorporates a critical plane approach. A quantitative verification of this criterion is carried out for different loading conditions and the results are compared with the experimental data available in the literature.     

部分输入未知条件下结构参数识别法研究

深入研究了输入信息测试不完备条件下的结构参数识别问题,从理论上论证了部分输入未知时动力复合反演问题补偿算法的实质,指出了全量补偿算法在严格意义上的适用条件,提出了更为简便的二阶段识别法,使部分输入未知条件下结构参数识别的理论进一步完善,并可为工程应用提供指导。数值算例验证了理论上的正确性。     

Damage,plasticity and failure of ceramics and cementitious composites subjected to multi-axial state of stress

Experimental data on mechanical behavior of ceramics and cementitious composites subjected to triaxial state of stress and verification of the theoretical model capable to describe deformability and fracture of brittle rock-like materials are presented in the paper. To check the validity of the theoretical model the stress–strain curves and stresses at material fracture determined experimentally for brick and mortar were compared with the theoretical predictions. The limit surface at material fracture obtained experimentally from triaxial tests was used in numerical analysis of masonry specimens subjected to compressive loading. These numerical results obtained by employing the Finite Element Method software package Mafem3D were compared with experimental data available in the literature. Fairly good agreement of numerical predictions with experimental results for masonry specimens was observed.     

Constitutive relations for a growing masonry with setting mortar

A model is proposed for averaging a periodic block structure, namely, a growing brick masonry body with setting interlayers of bonding mortar. The brick (block) material is assumed to be elastic, and the setting mortar is described by the model of an inhomogeneously aging viscoelastic medium. The obtained system of constitutive relations describes an anisotropic inhomogeneously aging viscoelastic medium and contains a small parameter that is the ratio of the hardening interlayer thickness to the brick thickness. Also presented is an example of solving the problem of erecting a brickwork (wall) deviating from the vertical in the gravity field.     

Characterization of a cohesive-zone model describing damage and de-cohesion at bonded interfaces. Sensitivity analysis and mode-I parameter identification

The identification of mode-I parameters of a cohesive-zone model for the analysis of adhesive joints is presented. It is based on an experimental–numerical methodology whereby the optimal parameters are obtained as the solution of a nonlinear programming problem. The data set for inverse analysis is provided either by local kinematic data, by global static data, or a combination of the two. Parameter sensitivities are computed via direct differentiation and identification exercises are discussed that show the effectiveness of the procedure and its stability with respect to noise and time–space sampling.     

A homogenized Love–Kirchhoff model for out-of-plane loaded random 2D lattices: Application to “quasi-periodic” brickwork panels

A homogenization procedure for finding the bending stiffness of a 2D regular lattice with random local interactions is proposed. The kinematic and static methods are used to provide explicit upper and lower bounds for the homogenized moduli. The proposed homogenization procedure is applied to a masonry obtained by a random perturbation of the periodic running bond masonry [Cecchi, A., Sab, K., 2009. Discrete and continuous models for in plane loaded random elastic brickwork. Eur. J. Mech. A 28, 610–625].A numerical evaluation of the scatter between the discrete models and the 2D Love–Kirchhoff model is performed on a test case, for various values of the random perturbation parameter and of the parameter that characterizes the heterogeneity of the wall. As expected, when the number of heterogeneities in the structure is large enough, the average response of the random discrete model converges to an asymptotic response. It is shown that this asymptotic response is very close to that of the periodic discrete model which is in turn very close to the response of the deterministic homogenized model. Similarly to the conclusion of Cecchi and Sab [Cecchi A., Sab K., 2009. Discrete and continuous models for in plane loaded random elastic brickwork. Eur. J. Mech. A. 28, 610–625.] dedicated to in-plane loading, the present results concerning out-of-plane loading show (both by means of a discrete model and a homogenized model) that the running bond pattern may be used successfully to analyze historical masonries with blocks having irregular widths in the horizontal direction.     

多孔砖砌体抗剪强度原位检测的试验研究

多孔砖砌体因具有节约土地能源资源,砌筑效率高,保温隔热和透气性能好等特点,目前已逐步成为砌体结构房屋的主要墙体材料。本文通过多孔砖砌体与标准试件抗剪强度的对比试验研究及试验结果的有限元分析,提出了多孔砖砌体抗剪强度原位双砖双剪的检测方法及其抗剪强度的计算公式。该方法可为多孔砖砌体结构房屋的可靠性评定、房屋建设、事故分析以及抗震加固等提供最基本的技术数据,为多孔砖砌体的应用与推广奠定了基础,并为砌体现场检测技术标准的补充修订提供了依据。     

Development of an approach to constitutive modelling of concrete: Isotropic damage coupled with plasticity

The paper presents an approach to constitutive modelling of concrete using damage mechanics and plasticity theory. The thermodynamic formulation, and parameter identification of a non-local coupled damage-plasticity model are presented in this study. The particular focus is the calibration of model parameters. It is shown that both the local parameters and the parameters governing the non-local interaction can be determined from experimental data reliably and consistently. A novel procedure is developed for parameter identification, using the separation of total dissipation energy into additive parts corresponding to different dissipation mechanisms. The relationship between the local and non-local parameters is also addressed, helping to obtain model responses consistent with the fracture energy of the material. The application of the model and the calibration procedure proposed in this study to the numerical failure analysis of concrete structures is illustrated through a series of real structural tests, showing both the performance of the model and the consistency of the proposed calibration procedure.     

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.     

Effect of non-linearities in the identification and fault detection of gear-pair systems

This study investigates issues related to parametric identification and health monitoring of dynamical systems with non-linear characteristics. In the first part, a gear-pair system supported on bearings with rolling elements is selected as an example mechanical model and the corresponding equations of motion are set up. This model possesses strongly non-linear characteristics, accounting for gear backlash and bearing stiffness non-linearities. Then, the basic steps of the parametric identification and fault detection procedure employed are outlined briefly. In particular, a Bayesian statistical framework is adopted in order to estimate the optimal values of the gear and bearing model parameters. This is achieved by combining experimental information from vibration measurements with theoretical information built into a parametric mathematical model of the system. In the second part of the study, characteristic numerical results are presented. First, based on the effect of the system parameters on its dynamics, a solid basis is created for explaining some of the peculiar results obtained by applying classical gradient-based optimization methodologies for the strongly non-linear system examined. Some serious difficulties, associated with the existence of irregular response or the coexistence of multiple motions, are first pointed out. A solution to some of these problems, through the application of a suitable genetic algorithm, is then presented. Special problems, related to more classical identification issues associated with the presence of measurement noise and model error, are also investigated.     

Determination of Ductile Damage Parameters by Local Deformation Fields: Measurement and Simulation

This work comprises the development, implementation and application of methods for the parameter identification of damage mechanical constitutive laws. Ductile damage is described on a continuum mechanical basis by extension of the von Mises yield condition with the Gurson–Tvergaard–Needleman as well as with the Rousselier model. The classical Rousselier model is complemented by accelerated void growth and void nucleation. The non-linear boundary and initial value problem is solved by the finite element system SPC–PMHP, which was developed in the frame of the special research program SFB393 for parallel computers. The material parameters are identified by locally measured displacement fields and measured force–displacement curves. For the material parameter identification a non-linear optimization algorithm is used, which renders the objective function to a minimum by means of a gradient based method. A useful strategy to identify the material parameters was found by careful numerical studies. Finally, using the object grating method the local displacement fields as well as the force–displacement curves are measured at notched flat bar tension specimens made of StE 690 and the parameters of the material are identified.     

Discrete and continuous models for in plane loaded random elastic brickwork

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.     

Homogenized rigid-plastic model for masonry walls subjected to impact

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.     

Parameter identification for improved viscoplastic model considering dynamic recrystallization

The successful application of viscoplastic model considering dynamic recrystallization depends on how well the parameters are identified. However, it is difficult to obtain satisfactory parameters using conventional parameter identification methods. The reasons are due to difficulties in obtaining homogeneous deformation, high complexity of physical process described by the model and large number of parameters. In this paper, the material parameters are identified by inverse analysis. Global information on objective function is firstly studied by an improved uniform random sampling method; secondly, a hybrid global optimization method, which combines the genetic algorithm, the Levenberg–Marquardt algorithm, the augmented Gauss–Newton algorithm and the flexible tolerance method, is constructed and an inverse analysis numerical procedure, which combines the proposed optimization method with the finite element analysis, is proposed; at last, a set of satisfactory material parameters for 26Cr2Ni4MoV is obtained by the proposed inverse analysis numerical procedure.     

High‐resolution,monotone solution of the adjoint shallow‐water equations

A monotone, second‐order accurate numerical scheme is presented for solving the differential form of the adjoint shallow‐water equations in generalized two‐dimensional coordinates. Fluctuation‐splitting is utilized to achieve a high‐resolution solution of the equations in primitive form. One‐step and two‐step schemes are presented and shown to achieve solutions of similarly high accuracy in one dimension. However, the two‐step method is shown to yield more accurate solutions to problems in which unsteady wave speeds are present. In two dimensions, the two‐step scheme is tested in the context of two parameter identification problems, and it is shown to accurately transmit the information needed to identify unknown forcing parameters based on measurements of the system response. The first problem involves the identification of an upstream flood hydrograph based on downstream depth measurements. The second problem involves the identification of a long wave state in the far‐field based on near‐field depth measurements. Copyright © 2002 John Wiley & Sons, Ltd.     

A homogenized Reissner–Mindlin model for orthotropic periodic plates: Application to brickwork panels

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.