An analytical study on the bond behaviour between an externally bonded FRP and concrete in the case of continuous beams

One of the greatest challenges in structural engineering nowadays is the strengthening, upgrading, and retrofitting of existing structures. The use of fibre-reinforced polymers (FRPs) bonded to the tension face of a structural member is an attractive technique in this field of application. The strengthening of reinforced concrete structures by means of an externally bonded reinforcement (EBR) is achieved by gluing a FRP laminate to the concrete substrate. For an efficient utilization of the FRP EBR systems, an effective stress transfer is required between the FRP and concrete. The paper discusses the bond behaviour between a FRP and concrete in the case of flexural strengthening of continuous beams. With respect to this type of beams, only a few studies have been reported, though continuous members often occur in concrete constructions. The structural behaviour of statically indeterminate elements is typically characterized by redistributions of the internal forces. These distributions are related to the nonlinear deformations of the beams and has also a distinct influence on the bond behaviour between the FRP and concrete. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 389–402, May–June, 2008.     

Modeling of the Behavior of Concrete Tension Members Reinforced with FRP Rods

The paper is devoted to the analysis of cracking and deformability of concrete tension members reinforced with fiber-reinforced polymer (FRP) rods. A theoretical nonlinear model, derived from a cracking analysis founded on slip and bond stresses, is adopted for evaluating the crack width, crack spacing, and elongation of tension members. The procedure takes into account the local bond-slip law, experimentally determined by means of pullout tests, and allows us to evaluate the influence of tensile stiffening. The analysis is performed with considering all parameters influencing the behavior of tension members, such as the concrete strength, the kind of FRP rebars, the surface treatment of FRP rebars, and the concrete cover thickness. The theoretical predictions are compared with available experimental results, obtained on cylindrical concrete specimens reinforced with carbon FRP (CFRP) rods, and with predictions of the traditional models usually adopted for design purposes.     

热防护服-空气-皮肤热传导模型及其解析解

建立了高温环境下热防护服-空气-皮肤的热传导模型.利用热传导时,层合界面间温度相等和热流量连续的条件,结合微分思想,用分离变量法推导了微小时间段内模型热传导的解析解,然后通过循环得到整个时域内的解析解.利用求得的解析解分析了在80℃的环境温度下模型各位置温度和热流密度的变化情况,以及在不同环境温度下皮肤表面温度变化和热...     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Extended Finite Element Method for hygro-mechanical analysis of crack propagation in porous materials

In computational structural analyses, strong discontinuities, such as propagating cracks in concrete structures, joints in rocks or shear bands in soft soils, the highly accelerated moisture transport in the opening discontinuities has to be taken into account. The paper is concerned with an Extended Finite Element model for the numerical representation of crack propagation in partially saturated porous materials. Based on an extended variational formulation for the simulation of moisture transport in cracks, enhanced approximations of the displacement field and the moisture flux across the discontinuity are adopted. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Problem with nonequilibrium boundary conditions in the kinetic theory of gases

The Boltzmann kinetic equation is considered in a new formulation with nonequilibrium distribution functions on free boundaries, which makes it possible to simulate nonequilibrium superand subsonic flows. Transport processes for such flows are analyzed. The possibility of anomalous transport is determined, in which case the heat flux, temperature gradient, and the corresponding components of the nonequilibrium stress tensor and the velocity gradient have the same sign.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.     

Variational Phase Field Modeling of Laminate Deformation Microstructure in Finite Gradient Crystal Plasticity

The macroscopic mechanical behavior of many materials crucially depends on the formation and evolution of their microstructure. In this work, we consider the formation and evolution of laminate deformation microstructure in plasticity. Inspired by work on the variational modeling of phase transformation [5] and building on related work on multislip gradient crystal plasticity [9], we present a new finite strain model for the formation and evolution of laminate deformation microstructure in double slip gradient crystal plasticity. Basic ingredients of our model are a nonconvex hardening potential and two gradient terms accounting for geometrically necessary dislocations (GNDs) by use of the dislocation density tensor and regularizing the sharp interfaces between different kinematically coherent plastic slip states. The plastic evolution is described by means of a nonsmooth dissipation potential for which we propose a new regularization. We formulate a continuous gradient-extended rate-variational framework and discretize it in time to obtain an incremental-variational formulation. Discretization in space yields a finite element formulation which is used to demonstrate the capability of our model to predict the formation and evolution of laminate deformation microstructure in f.c.c. Copper with two active slip systems in the same slip plane. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational homogenization of non-stationary transport processes in masonry structures

A fully coupled transient heat and moisture transport in a masonry structure is examined in this paper. Supported by several successful applications in civil engineering the nonlinear diffusion model proposed by Künzel (1997) [16] is adopted in the present study. A strong material heterogeneity together with a significant dependence of the model parameters on initial conditions as well as the gradients of heat and moisture fields vindicates the use of a hierarchical modeling strategy to solve the problem of this kind. Attention is limited to the classical first order homogenization in a spatial domain developed here in the framework of a two step (meso–macro) multi-scale computational scheme (FE² problem). Several illustrative examples are presented to investigate the influence of transient flow at the level of constituents (meso-scale) on the macroscopic response including the effect of macro-scale boundary conditions. A two-dimensional section of Charles Bridge subjected to actual climatic conditions is analyzed next to confirm the suitability of algorithmic format of FE² scheme for the parallel computing.     

A model of the heat conduction for functionally graded laminate with uniformly distributed micro inclusions

The aim of the contribution is to formulate an asymptotic model of heat conduction for functionally graded two component laminate reinforced by periodically spaced micro inclusions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Coupled heat and moisture transport in paper with application to a warm print surface

In this work we present a mathematical model describing the coupled heat and moisture transport in paper. The model is solved numerically and the numerical solution is used to study the interdependency of the moisture and temperature distribution in paper. The results show that variation with temperature of the saturated water vapor concentration and the sorption isotherm parameters are both important for inducing moisture desorption. It is also found that for steep relative humidity ramps moisture sorption generates temperature increments that slow down the sorption process itself. The model is also used to study the moisture gradients in a paper sheet inside a printer from Océ Technologies, which contains a warm print surface. The results predict changes in moisture content of only 0.2%, which suggests that no deformations are induced on the printed sheet.     

Modeling of thermal response and ablation in laminated glass fiber reinforced polymer matrix composites due to lightning strike

Thermal response and ablation of laminated glass fiber reinforced polymer matrix composites subjected to lightning strike are studied. The associated nonlinear time-dependent heat transfer model includes specific features of lightning arcs observed in physical measurements such as lightning channel radius expansion, non-uniform lightning current density, and associated heat flux. Moving spatially and temporally non-uniform lightning-current-induced heat flux boundary and moving boundary due to material phase transition caused by rapid surface ablation are also included. To predict moving phase boundary in the laminated anisotropic composites, an element deletion method is developed and embedded into finite element analysis (FEA), which is performed using ABAQUS. The Umeshmotion + ALE method based on the user subroutine Umeshmotion and arbitrary Lagrangian–Eulerian (ALE) adaptive mesh technique is also used, when applicable (i.e., moving phase boundary is confined within a top layer of the composite laminate). Heat transfer analysis is performed for a non-conductive laminated glass fiber reinforced polymer matrix composite panel representing the SNL 100-00 wind turbine tip. Thermal response of the panel subjected to pulsed and continuing lightning currents at three different lightning protection levels, LPL I, LPL II, and LPL III, is studied. Temperature-dependent anisotropic thermal properties of the composite panel are included in the analysis. The FEA results include temperature distributions and ablation zone profiles. The results show the Umeshmotion + ALE method is sufficient for the pulsed lightning current at all three LPL levels since the moving phase boundary, i.e. the ablation front, is found to be confined within the top layer of the laminate. For the continuing lightning currents at all three LPL levels, the Umeshmotion + ALE method is not applicable since the moving phase boundary comes to rest at depths exceeding the thickness of the top layer of the composite laminate.     

Numerical Solution of the Kiessl Model

The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE's. Some existence and regularity results for these problems are proved and an efficient numerical approach based on a certain special linearization scheme and the Petrov-Galerkin method is suggested.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.Department of Materials Science, University of Lecce, Via per Arnesano, 73100 Lecce, Italy. Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 163–172, March–April, 1999.     

Environmental Effects on the Mechanical Properties of Glass-FRP and Aramid-FRP Rebars

In the paper, the experimental results on the effect of temperature and moisture on the mechanical properties of FRP (Fiber-Reinforced Polymer) reinforcements are presented. FRP rebars made from glass and aramid fibers were subjected to cyclic thermal actions at temperatures ranging between 20 and 70°C, typical of natural hot-climate environments. Tensile tests were also carried out on FRP rebars. The effect of moisture was investigated by cyclic wetting and drying the FRP rebars under laboratory conditions before their testing in tension. Finally, the elastic modulus and tensile strength of the FRP rebars exposed to these cyclic actions were compared with those obtained for unexposed ones, in order to evaluate the mechanical damage caused by environmental conditions.     

A finite element model for the fire-performance of GRP panels including variable thermal properties

A finite element study is conducted to determine the thermal response of a widely used glass reinforced plastic panel exposed to fire. This study is performed based on a formulation developed previously by the authors and improved by including the moisture and temperature-dependent thermal properties and a newly developed time-dependent non-linear mixed boundary condition at the unexposed surface of the panel. In addition, the influence of non-zero final resin mass is considered according to a recently performed thermal gravimetric analysis. In order to derive the appropriate element equations, a mixed explicit–implicit Bubnov–Galerkin finite element approach is adopted. Results of this study are presented for a standard, 10.9 mm, thickness of single-skinned polyester-based glass reinforced plastic panel and comprise temperature profiles, density distributions and moisture profiles. Comparisons are made between the predicted results and those obtained experimentally. The predicted temperatures agreed with the experimental results with an average difference of 21.41°C. A simple comparison of the present value with that of the authors’ previous model, 29.66°C, indicates a considerable improvement of 38.53% in the fire-performance prediction of the material.     

Effect of shear stiffness and concrete wedge cone failure on fracture of a fiber-reinforced plastic rod at an intersection with a concrete crack

Experimental results of model speciments in which FRP rods fractured due to local deformation at a crack intersection in a concrete member were analyzed by a 3D nonlinear finite element method in which orthogonal anisotropy of the FRP rod was considered. The analytical results indicated that accurate prediction of shear modulus of the FRP rod and size of concrete wedge cone failure around the FRP rod was significant to predict deformation and fracture of the FRP rod. FRP rods as reinforcement in concrete members, the small shear modulus, because of the orthogonal anisotropy and the wedge cone failure, may prevent the FRP rod from fracturing at a very low tensile stress due to the local deformation at the crack intersection.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 21, No. 2, pp. 158–166, March–April, 1996.     

Bond of FRP Reinforcement in Concrete - a Challenge

The bond of ordinary steel reinforcement in concrete depends on many factors, such as the pullout resistance, the geometry of a concrete member, the placement of a bar in the member cross section, the cover splitting, the confinement caused by concrete and the surrounding reinforcement, the order of bond-crack appearance, and the bond-stress distribution along the bond length. The bond of FRP reinforcement depends on even a greater number of factors. Moreover, the types of FRP bars are numerous. Their surface is weaker than that of steel bars and may fracture by bond forces. The surface of FRP bars is softer and does not create as high local stress concentrations in bond contact points to concrete as the harder steel bars do. This fact often delays the appearance of cover splitting cracks along the bars. However, the load necessary for developing the crack pattern of ultimate splitting failure in concrete is then very dependent on whether the bar surface is glossy or rough. The FRP reinforcement can also be used for external shear and/or flexural strengthening of existing members. For this application, FRP bars are placed in grooves cut on the surface of the member to be strengthened and are fixed there with a cement mortar or epoxy paste. In such an application, the performance of bond between the FRP rod and the mortar or resin and then between the mortar or resin and concrete is critical for the effectiveness of the technique. The presence of two interfaces increases the number of parameters needed to characterize the global joint behavior and introduces new possible failure modes. The fundament for the bond resistance estimation should be an accepted bond philosophy linked to appropriate models. A system of bond tests should provide necessary coefficients for the models.     

Nonlinear flexural response of laminated composite plates under hygro-thermo-mechanical loading

The paper deals with Chebyshev series based analytical solution for the nonlinear flexural response of the elastically supported moderately thick laminated composite rectangular plates subjected to hygro-thermo-mechanical loading. The mathematical formulation is based on higher order shear deformation theory (HSDT) and von-Karman nonlinear kinematics. The elastic foundation is modeled as shear deformable with cubic nonlinearity. The elastic and hygrothermal properties of the fiber reinforced composite material are considered to be dependent on temperature and moisture concentration and have been evaluated utilizing micromechanics model. The quadratic extrapolation technique is used for linearization and fast converging finite double Chebyshev series is used for spatial discretization of the governing nonlinear equations of equilibrium. The effects of Winkler and Pasternak foundation parameters, temperature and moisture concentration on nonlinear flexural response of the laminated composite rectangular plate with different lamination scheme and boundary conditions are presented.