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.     

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.     

Nonlinear parameter identification of models for masonry

This paper investigates the parameter estimation problem for brick masonry models. An identification procedure is proposed in which the uncertainties of known parameters and/or errors of measurements are its elements of distinction. The minimization process of the discrepancies between experimental data and theoretical measurements takes place by means of a first order iterative method. The identification procedure is applied to two different problems: the calibration of an interface model for brick–mortar joint in its functional form through monotonic experimental tests; to evaluate the unknown parameters of a continuum model for brick masonry walls in its non-holonomic form by means of in-plane cyclic shear–compression test of masonry panels. The general framework of the non-linear estimate methodology, the parameter identification problems and the numerical results are presented.     

燃气爆炸作用下蒸压加气混凝土砌体墙的加固性能

为研究燃气爆炸作用下蒸压加气混凝土砌体墙的加固性能,基于有限元软件LS-DYNA,建立了砌体墙简化数值模型,分析了GB 50779-2012 石油化工控制室抗爆设计规范中建议的荷载作用下砌体墙高度和厚度的影响,对比了玄武岩纤维(basalt fiber reinforced plastic, BFRP)布与喷涂式聚脲对蒸压加气混凝土单向砌体墙的加固效果,并以防止砌体墙倒塌为设计目标,给出了加固建议。研究表明,本文中建立的简化数值模型能较好地模拟燃气爆炸作用下蒸压加气混凝土砌体墙的变形和破坏模式,计算结果与试验吻合良好;《规范》建议荷载作用下,未加固砌体墙以弯曲破坏为主,随着墙体高度增加,破坏模式由弯曲破坏向剪切破坏转变;BFRP布条加固可以有效提高墙体抗弯刚度和压拱效应,而聚脲涂层加固对抗弯刚度提高有限但墙体拉拱效应明显,二者均能显著提高墙体抗爆性能;加固墙体均发生弯曲破坏,BFRP布条材料的断裂一般发生在墙体位移最大处,而聚脲涂层材料的断裂发生在跨端边界处。     

爆炸载荷下仿贝壳结构的动态响应

贝壳珍珠层是一种具有高强度和高韧性的天然材料,这种优异的性能主要来源于多尺度、多层级的“砖泥”结构。本文受贝壳特殊结构的启发,构建了仿贝壳砖泥结构的有限元模型,并进行了爆炸实验。通过实验发现:在爆炸冲量为0.047 N·s时,试件发生灾难性破坏,使得中心处发生掉落,且伴随着试件夹持端的剪切破坏,与数值模拟结果具有良好的一致性。在实验基础上,对仿贝壳砖泥结构在爆炸载荷下的动态响应进行了数值模拟。研究发现,在爆炸载荷下仿贝壳砖泥结构会产生五种不同的破坏模式,包括:Ⅰ,结构整体无损伤;Ⅱ,结构前表面无明显破坏,后表面发生破坏;Ⅲ,结构发生掉落型贯穿破坏,夹持端无剪切破坏;Ⅳ,结构发生小块掉落型贯穿破坏,夹持端发生剪切破坏;Ⅴ,结构发生大块掉落型贯穿破坏,夹持端发生剪切破坏。并且给出了不同破坏模式的临界阈值,单层砖泥结构的破坏阈值为0.019 N·s,五层砖泥结构的破坏阈值为0.047 N·s,当冲量超过破坏阈值时,试件发生灾难性破坏。研究分析了堆叠层数对仿生结构的力学响应,在同一冲量下,随着层数的增加,结构的破坏模式发生改变,由贯穿型破坏逐渐变为仅发生一定塑性变形。随着层数增加,结构的损伤阈值增加。最后提出仿贝壳砖泥结构的增韧机理主要有裂纹偏转和微裂纹。     

Masonry walls strengthened with composite materials – dynamic out-of-plane behavior

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.     

爆炸冲击震动对砖墙破坏作用的数值模拟

砖墙在爆炸冲击震动作用下的动力反应非常复杂,本构关系很难精确建立。本文阐述了砖墙几种常用的有限元模拟方法,分析各种方法的优缺点,确定采用一种砖块和砂浆分开的精细化建模的三维砖墙有限元模型;通过LS-DYNA软件,得到砖墙在水平爆炸冲击震动荷载下的破坏过程,计算结果与实验现象很好。研究表明:该种分析模型综合考虑了砖块和砂浆之间复杂的相互作用,并且对砂浆层进行了单独建模,保证了砖墙在数值模拟上的真实性和正确性,因此可以准确地模拟出实验中砖块之间砂浆层的损伤积累破坏。     

Compatible model for herringbone bond masonry: Linear elastic homogenization,failure surfaces and structural implementation

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.     

Experimental investigations of the joint-mortar behaviour

An important failure mode of the masonry walls is the shearing process in joint mortar. In order to understand better this phenomenon, an experimental study is carried out on half brick couplet specimen. Load/Unload shear tests are performed to assess the type of the shear behaviour of the joint mortar. The cohesion and the internal friction angle are then derived from linear regression while assuming Mohr–Coulomb criterion. In particular, the influence of holes on the joint behaviour is studied by comparing results obtained with both solid and hollow bricks. In both cases, the experimental results show that there is not any stiffness degradation even in the softening regime. Actually, the shear modulus remains constant. Hence, the joint behaviour is considered to be elastoplastic, independently on the brick type. However, it seems that the presence of holes increases the stiffness but does not affect the internal friction angle of the joint mortar.     

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.     

砌体填充墙的抗爆性能

为了揭示砌体填充墙的抗爆破坏机理,在野外实验中,测得了爆炸条件下砌体填充墙上的爆炸荷载及位移,得到了墙的抗爆性能、破坏模式以及碎片的飞散和分布情况。实验结果表明,墙体的破坏模式与荷载的大小有关,其破坏主要由灰缝的破坏引起。结合实验现象,采用分离式建模的精细化数值模拟方法,得到了不同荷载条件下裂缝的发展过程、墙体的边界条件对墙体的破坏模式的影响,确定了墙体不同破坏等级时的药量,进一步说明本文中数值模拟方法的合理性。     

A homogenized viscoelastic model for masonry structures

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.     

Dynamic mechanical and fracture properties of an infiltrated TiC-1080 steel cermet

The dynamic mechanical and fracture properties of a TiC porous network infiltrated with1080 steel are reported. Following infiltration, the cermet is subjected to various heat treatments that affect essentially the steel matrix. Dynamic compression tests show that the heat treatments increase the fracture strength of the cermet. The quasi-static fracture toughness (K_Ic) is also increased by the heat treatments. The dynamic (initiation) fracture toughness (K_Id) is substantially higher (by about a factor of 3) than its static counterpart. Failure mechanisms consist mainly of cleavage of the TiC and matrix grains, along with minor interfacial decohesion. However, dynamic loading induces substantial damage around the crack tip, consisting essentially of cleavage of TiC grains. Microcrak toughnening is believed to be responsible for the high dynamic toughness of the material. The critical microstructural fracture event is thus identified as the spreading of TiC cleavage microcracks into the neighboring steel grains.     

基于分离式建模的砖石古塔动力性能与响应分析

为研究砖石古塔的动力特性及地震响应机制,以渭南慧照寺塔为对象,采用块体-灰浆分区离散方法,分别建立刚性地基条件与考虑地基-结构相互作用条件下古塔的数值模型,计算比较了塔体的动力特性;并分别按9度小震、中震和大震输入El-Centro波、Taft波和兰州人工波,计算了结构的位移和加速度反应,与相互作用系统进行比较。结果表明,考虑土-结构相互作用后,古塔结构的一阶自振频率降低5.7%,二阶频率降低45%;El-Centro波和Taft波作用下,位移和加速度响应显著增大,大震作用时,与不考虑土-结构相互作用对比,主拉应力峰值显著增加,古塔从灰浆开裂发展为砖与灰浆同时开裂;兰州人工波作用下,考虑土-结构相互作用后,主拉应力和结构开裂变形反而降低。研究结果可为古塔抗震计算与性能评估提供参考。     

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.     

Finite element analyses of cracks in piezoelectric structures: a survey

Piezoelectric materials have widespread applications in modern technical areas such as mechatronics, smart structures or microsystem technology, where they serve as sensors or actuators. For the assessment of strength and reliability of piezoelectric structures under combined electrical and mechanical loading, the existence of cracklike defects plays an important role. Meanwhile, piezoelectric fracture mechanics has been established quite well, but its application to realistic crack configurations and loading situations in piezoelectric structures requires the use of numerical techniques as finite element methods (FEM) or boundary element methods (BEM). The aim of this paper is to review the state of the art of FEM to compute the coupled electromechanical boundary value problem of cracks in 2D and 3D piezoelectric structures under static and dynamic loading. In order to calculate the relevant fracture parameters very precisely and efficiently, the numerical treatment must account for the singularity of the mechanical and electrical fields at crack tips. The following specialized techniques are presented in detail (1) special singular crack tip elements, (2) determination of intensity factors K _I –K _IV from near tip fields, (3) modified crack closure integral, (4) computation of the electromechanical J-integral, and (5) exploitation of interaction integrals. Special emphasis is devoted to a realistic modeling of the dielectric medium inside the crack, leading to specific electric crack face boundary conditions. The accuracy, efficiency, and applicability of these techniques are examined by various example problems and discussed with respect to their advantages and drawbacks for practical applications.     

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.     

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.     

A nonlinear homogenization procedure for periodic masonry

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.