A nonlinear viscoelastic fracture analysis of concrete/FRP delamination in aggressive environments

In this paper, the durability of the bondline between concrete and FRP reinforcement was characterized at various temperature and humidity levels. The linear and nonlinear viscoelastic constitutive behavior of the epoxy bondline was characterized and used for a nonlinear viscoelastic fracture analysis of delamination. A hygrothermal nonlinear viscoelastic pseudo-stress model was developed and calibrated in order to compute a generalized J integral. Driven wedge tests were conducted for examining the fracture behavior of the interface. A finite element analysis was developed for determining the cohesive zone size and the generalized J integral at various temperature and humidity levels. The fracture energy obtained from these parameters greatly depended upon crack growth rate, temperature and humidity.     

A geometrically exact formulation for thin multi-layered laminated composite plates: Theory and experiment

A geometrically exact approach is employed to formulate the equations of motion of thin multi-layered isotropic and laminated composite plates subject to excitations that cause large strains, displacements, and rotations. The linearization of the obtained semi-intrinsic theory leads to the Mindlin–Reissner theory while an ad hoc truncated kinematic approximation delivers, as a by-product, the Föppl–von Kármán theory of plates. An experimental validation is sought for fully clamped plates which are either of the isotropic single-layered type or of the multi-layered laminated composite type. To this end, nonlinear equilibrium paths are constructed both theoretically and experimentally when the plates are subject to a quasi-statically increasing central point load. The comparisons between the experimentally obtained results and those furnished by the geometrically exact theory as well as by the Föppl–von Kármán (FVK) theory show the high accuracy of the proposed nonlinear theory while the FVK theory becomes increasingly inaccurate at deflection amplitudes of the order of the plates thickness.     

Stress analysis of multi-bolted joints for FRP pultruded composite structures

In the last decades, FRP composites have been widely used for constructing entire civil structures. One of the challenging issues for building with pultruded FRP composites is understanding the behaviour of bolted joints. In this paper, the results of a numerical analysis performed on different types of bolted composite joints with different geometry and subjected to tensile loads are reported. The aim of this study is to examine the distribution of shear stresses among the different bolts by varying the number of rows of bolts as well as the number of bolts per row. The study also considers the presence of variable diameter washers and their influence on the bearing stresses of composites with different fibre orientations. For verification of the validity of the analytical models, numerical results are compared to experimental results reported elsewhere. The results of this study showed that in multi-bolt joints, the load is not distributed equally due to varying bolt position, bolt-hole clearance, bolt-torque or tightening of the bolt, friction between member plates and at washer-plate interface. The results also indicated that in the presence of washers, the stress distributions in the fibre direction, varying fibre inclinations, are decreasing for each value of washer pressure.     

Implementation of a constitutive micromechanical model for damage analysis in glass mat reinforced composite structures

A micromechanical model based on a probabilistic approach is implemented in the finite element code CASTEM 2000 to develop numerical simulations that efficiently predict the overall damaged behaviour of random oriented fibre composites. The proposed damage constitutive model is based upon the generalised Mori and Tanaka scheme and Eshelby's equivalence theory. Damage mechanisms occurring at each composite constituent (fibres, matrix and interface) are associated to Weibull probabilistic functions to model their onset and progressive growth at the microscopic scale level. It is obvious that the damaged behaviour of the composite material depends widely on the microscopic material parameters (fibre length, fibre volume fraction, fibre orientation, …). On one hand, the micromechanical model uses homogenisation techniques which enabled us to link these microscopic parameters to the material behaviour and to evaluate explicitly their influences. On the other hand, the implementation of the derived behaviour law into a finite element code enabled us to reflect on the effect of these microscopic parameters on the overall response of a simple composite structure presenting heterogeneous stress fields. In fact, the damage evolution in each constituent (local scale) and the related stiffness reduction are estimated at any material point (integration point) or node of the considered structure subject to a specific loading. Numerical simulations of a composite plate with a hole under in-plane tension were performed to validate the implementation of the behaviour law. Numerical results have been compared to experimental curves and damage evolutions monitored by acoustic emission techniques. Simulations agree well with experimental results in terms of damage onset and growth.     

Finite element analysis of viscoelastic composite structures based on a micromechanical material model

The stress and creep analysis of structures made of micro-heterogeneous composite materials is treated as a two-scale problem, defined as a mechanical investigation on different length scales. Reinforced composites show by definition a heterogeneous texture on the microlevel, determined by the constitutive behaviour of the matrix material and the embedded fibres as well as the characteristics of the bonding properties in the interphase. All these heterogeneities are neglected by the finite element analysis of structural elements on the macroscale, since a ficticious and homogeneous continuum with averaged properties is assumed. Therefore, the constitutive equations of the substitute material should well reflect the mechanical behaviour of the existing micro-heterogeneous composite in an average sense.The paper at hand starts with the brief outline of a micromechanical model, named generalized method of cells (GMC), which provides the macrostress responses due to macrostrain processes as well as the homogenised constitutive tensor of the substitute material. The macroscopic stresses and strains are obtained as volume averages of the corresponding microfields within a representative volume element. The effective material tensor constitutes the mapping between the macro-strains and the macro-stresses. The cells method is used for the homogenisation of the unidirectionally reinforced single layers of laminates made of viscoelastic resins and flexibly embedded elastic fibres. The algorithm for the homogenisation of the constitutive properties runs simultaneously to the finite element analysis at each point of numerical integration and provides the macro-stresses and the homogenised constitutive properties. The validity of the proposed two-scale simulation is investigated by solving boundary value problems and comparing the numerical results for the structures to the experimental data of creep and relaxation tests or analytical solutions.     

Sensitivity analysis of frequency response functions of composite sandwich plates containing viscoelastic layers

In the scope of structural dynamics, sensitivity analysis is a very useful tool in a number of numerical procedures such as parameter identification, model updating, optimal design and uncertainty propagation. In this paper the formulation of first-order sensitivity analysis of complex frequency response functions (FRFs) is developed for composite sandwich plates composed by a combination of fiber-reinforced and elastomeric viscoelastic layers, in arrangements that are frequently used for the purpose of noise and vibration attenuation. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to viscoelastic structures, which are characterized by frequency- and temperature-dependent material properties and, thus, require particularly adapted analytical and numerical procedures. Due to the fact that finite element discretization has become the most used method for dynamic analysis of complex structures, the sensitivity analysis addressed herein is based on such models, being computed from the analytical derivatives of the FRFs with respect to a set of design parameters, such as fiber orientations and layer thicknesses. Also, a procedure for evaluating the sensitivity of the FRFs with respect to temperature of the viscoelastic material is suggested. After discussion of various theoretical aspects, including a parameterization scheme of the structural matrices with respect to the design variables, first-order response derivatives are calculated for a composite plate with inherent structural damping, and for a composite sandwich plate with a viscoelastic core. The results are compared to those obtained from first-order finite-difference approximations.     

Stress analysis of multi-layered hollow anisotropic composite cylindrical structures using the homogenization method

This paper presents a general and efficient stress analysis strategy for hollow composite cylindrical structures consisting of multiple layers of different anisotropic materials subjected to different loads. Cylindrical material anisotropy and various loading conditions are considered in the stress analysis. The general stress solutions for homogenized hollow anisotropic cylinders subjected to pressure, axial force, torsion, shear and bending are presented with explicit formulations under typical force and displacement boundary conditions. The stresses and strains in a layer of the composite cylindrical structures are obtained from the solutions of homogenized hollow cylinders with effective material properties and discontinuous layer material properties. Effective axial, torsional, bending and coupling stiffness coefficients taking into account material anisotropy are also determined from the strain solutions for the hollow composite cylindrical structures. Examples show that the material anisotropy may have significant effects on the effective stiffness coefficients in some cases. The stress analysis method is demonstrated with an example of stress analysis of a 22-layer composite riser, and the results are compared with numerical solutions. This method is efficient for stress analysis of thin-walled or moderately thick-walled hollow composite cylindrical structures with various multiple layers of different materials or arbitrary fiber angles because no explicit interfacial continuity parameters are required. It provides an efficient and easy-to-use analysis tool for assessing hollow composite cylindrical structures in engineering applications.     

A nonlinear double-superposition global–local theory for dynamic buckling of imperfect viscoelastic composite/sandwich plates: A hierarchical constitutive model

Nonlinear dynamic thermo-mechanical buckling and postbuckling analyses of imperfect viscoelastic composite laminated/sandwich plates are performed by a proposed theory that takes into account all the interlaminar kinematic and transverse stress continuity conditions, for the first time. Even the dynamic buckling analysis of the multi-layered/sandwich plates employing the hierarchical constitutive model has not been performed before. The proposed theory is a double-superposition high-order global–local theory that is calibrated based on the nonlinear strain–displacement expressions for the thermoelastic loadings taking into account the structural damping. The buckling loads are determined based on a criterion previously published by the author. Various complex sensitivity analyses evaluating effects of the relaxation parameters, rate of the loading, sudden heating, and pre-stress on thermo-mechanical buckling of the viscoelatic multi-layered/sandwich plates are performed. Results show that the viscoelastic behavior may decrease the buckling load. Sudden dynamic buckling loads are higher due to the reflected stress waves.     

Vibration and damping analysis of a three-layered composite annular plate with a viscoelastic mid-layer

The natural frequencies and modal loss factors of the three-layered annular plate with a viscoelastic core layer and two polar orthotropic laminated face layers are considered. The discrete layer annular finite element is employed to derive the equations of motion for the three-layered annular plate. The viscoelastic material in the central layer is assumed to be incompressible, and the extensional and shear moduli are described by the complex quantities. Complex eigenvalued problems are then solved, and the frequencies and modal loss factors of the composite plate are extracted. The results of the symmetric and non-symmetric composite annular plates are both presented. The effects of material properties, radius to thickness ratio, stacking sequences and thickness of face layers, and thickness of the viscoelastic core layer are discussed.     

Dynamic analysis and damping of composite structures embedded with viscoelastic layers

In recent years, it has been found that composites co-cured with viscoelastic materials can enhance the damping capacity of a composite structural system with little reduction in stiffness and strength. Because of the anisotropy of the constraining layers, the damping mechanism of co-cured composites is quite different from that of conventional structures with metal constraining layers. This paper presents an analysis of the dynamic properties of multiple damping layer, laminated composite beams with anisotropic stiffness layers, by means of the finite element-based modal strain energy method. ANSYS 4.4A finite element software has been used for this study. The variation of resonance frequencies and modal loss factors of various beam samples with temperature is studied. Some of these results are compared with the closed-form theoretical results of an earlier published work. For obtaining optimium dynamic properties, the effects of different parameters, such as layer orientation angle and compliant layering, are studied. Also, the effect of using a combination of different damping materials in the system for obtaining stable damping properties over a wide temperature range is studied.     

The quasi-static analysis for the viscoelastic hollow circular cylinder using the symplectic system method

The symplectic system method is introduced into the quasi-static analysis for axial symmetric problems of the viscoelastic hollow circular cylinder, with the emphasis on the local effects. By employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained directly. The combinations of the eigenvectors can describe the classical Saint-Venant problems and the local effects near the boundary. After constructing the adjoint symplectic relationships between the eigenvectors, the symplectic system method can be applied to solve quasi-static viscoelastic problems by expanding the eigenvectors to satisfy the given boundary conditions. Numerical results show the local effects due to the displacement constraints and the creep phenomenon of the time dependent material under certain boundary conditions. The results obtained by the approach are accurate, because all the given lateral boundary conditions and end conditions of the cylinder can be satisfied.     

Experimental investigation of the dynamic response of graphite-epoxy composite laminates under compression

In this study, the dynamic stress–strain response of graphite-epoxy composite laminates is investigated. The laminates are interposed in a section of a split Hopkinson apparatus. A quasi-rectangular wave is generated at one end of the incident bar by striking it with another bar of known length. This bar is accelerated using a compressed air gun. Approximate average stresses and strains can be obtained by measuring the incident, reflected and transmitted waves in the split bar. The dynamic behavior is evaluated for a range of impact velocities. The dependence of the response on impact velocity is analyzed and discussed. Three different specimen thicknesses have been used. These are obtained by increasing the repetition factor of a base stacking sequence: (+45°, −45°, 0°, 90°). This process is called sublaminate scaling; it is preferred to ply scaling since it has been shown that the accumulation of layers of the same orientation decreases the failure load to such an extent that residual stresses may crack the specimen before any external load is applied. The laminates considered are: (+45°, −45°, 0°, 90°)_ns, n=2,3,4. The scale effects observed in the experimental response are analyzed and discussed.     

A numerical study of free and forced vibration of composite sandwich beam with viscoelastic core

In this article, higher order theory for sandwich beam with composite faces and viscoelastic core is achieved by considering independent transverse displacements on two faces and linear variations through the depth of the beam core. In addition, the effects of Young modulus, rotational inertia and core kinetic energy are considered to modify the “Mead & Markus” theory that is used frequently for sandwich beam. These assumptions have not been considered together in previous articles. A finite element code is developed for structural response analysis of the free and forced vibration. The obtained results are compared with the corresponding results of previous researches. The effects of impressive parameters including fiber angle, thickness of faces and core thickness on the loss factors and natural frequencies of the beam are examined. Frequency response of the beam for two cases, constant and frequency dependent core shear modulus are obtained. Finally, time response of the beam is presented based on the Newmark method. Obtained results show that, when the core is soft or hard, “Mead & Markus” theory cannot accurately predict the frequency responses of the system in comparison with the presented theory in this paper; whereas for moderately hard core, both methods lead to the same results. In addition, when the beam is unsymmetrical about its neutral axis, i.e. one face sheet is weaker than the other face sheet, the inaccuracy of the “Mead & Markus” theory increases, even at low frequencies.     

Estimation of piezoelastic and viscoelastic properties in laminated structures

An inverse method for material parameter estimation of elastic, piezoelectric and viscoelastic laminated plate structures is presented. The method uses a gradient based optimization technique in order to solve the inverse problem, through minimization of an error functional which expresses the difference between experimental free vibration data and corresponding numerical data produced by a finite element model. The complex modulus approach is used to model the viscoelastic material behavior, assuming hysteretic type damping. Applications that illustrate the influence of adhesive material interfaces and viscoelastic parameter identification are presented and a few simulated test cases aid the interpretation of results.     

A generalized micromechanical approach for the analysis of transverse crack and induced delamination in composite laminates

The previously developed micromechanical approaches for the analysis of transverse cracking and induced delamination are limited for laminates with specific lay-ups such as cross-ply and specific loading conditions. In this paper a new micromechanical approach is developed to overcome such shortcomings. For this purpose, a unit cell in the ply level of composite laminate including transverse cracking and delamination is considered. Then, the governing equations for the stress and displacement fields of the unit cell are derived. The obtained approximate stress field is used to calculate the energy release rate for the propagation of transverse cracking and induced delamination. To show the capability of the new method, it is employed for the analyses of general laminates with [0/90]_s, [45/−45]_s, [30/−30]_s and [90/45/0/−45]_s lay-ups under combined loadings to calculate the energy release rate due to the transverse cracking and induced delamination. It is shown that the obtained energy release rates for transverse cracking and delamination initiation are in good agreement with the available results in the literature and finite element method. Furthermore, the occurrence priority of further transverse cracks and/or delamination at each damage state of the laminates will be discussed.     

Optimal design and parameter estimation of frequency dependent viscoelastic laminated sandwich composite plates

Recent developments in optimization and parameter estimation of frequency dependent passive damping of sandwich structures with viscoelastic core are presented in this paper. A finite element model for anisotropic laminated plate structures with viscoelastic frequency dependent core and laminated anisotropic face layers has been formulated, using a mixed layerwise approach, by considering a higher order shear deformation theory (HSDT) to represent the displacement field of the viscoelastic core, and a first order shear deformation theory (FSDT) for the displacement fields of adjacent laminated face layers. The complex modulus approach is used for the viscoelastic material behaviour, and the dynamic problem is solved in the frequency domain, using viscoelastic material data for the core, assuming fractional derivative constitutive models. Constrained optimization of passive damping is conducted for the maximisation of modal loss factors, using the Feasible Arc Interior Point Algorithm (FAIPA). Identification of the frequency dependent material properties of the sandwich core is conducted by estimating the parameters that define the fractional derivative constitutive model. Optimal design and parameter estimation applications in sandwich structures are presented and discussed.     

On the use of a spectrum-based model for linear viscoelastic materials

A new spectrum-based model for describing the behavior of time-dependent materials is presented. In this paper, unlike most prior modeling techniques, the time-dependent response of viscoelastic materials is not expressed through the use of series. Instead, certain criteria have been imposed to select a spectrum function that has the potential of describing a wide range of material behavior. Another consequence of choosing the spectrum function of the type used in this paper is to have a few closed form analytic solutions in the theory of linear viscoelasticity. The Laplace transform technique is used to obtain the necessary formulae for viscoelastic Lame' functions, relaxation and bulk moduli, creep bulk and shear compliance, as well as Poisson's ratio. By using the Elastic–Viscoelastic Correspondence Principle (EVCP), material constants appearing in the proposed model are obtained by comparing the experimental data with the solution of the integral equation for a simple tensile test. The resulting viscoelastic functions describe the material properties which can then be used to express the behavior of a material in other loading configurations. The model's potential is demonstrated and its limitations are discussed.     

A numerical integration approach for fractional-order viscoelastic analysis of hereditary-aging structures

In this paper, a novel numerical integration scheme is proposed for fractional-order viscoelastic analysis of hereditary-aging structures. More precisely, the idea of aging is first introduced through a new phenomenological viscoelastic model characterized by variable-order fractional operators. Then, the presented fractional-order viscoelastic model is included in a variational formulation, conceived for any viscous kernel and discretized in time by employing a discontinuous Galerkin method. The accuracy of the resulting finite element (FE) scheme is analyzed through a model problem, whose exact solution is known; and the most significant variables affecting the solution quality, such as the number of Gaussian quadrature points and time subintervals, are then investigated in terms of error and computational cost. Moreover, the proposed FE integration scheme is applied to study the short- and long-term behavior of concrete structures, which, due to the severe aging exhibited during their service life, represents one of the most challenging time-dependent behavior to be investigated. Eventually, also the Euler implicit method, commonly used in commercial software, is compared.     

A combined elastoplastic damage model for progressive failure analysis of composite materials and structures

The paper is concerned with the development and verification of a combined elastoplastic damage model for the progressive failure analysis of composite materials and structures. The model accounts for the irreversible strains caused by plasticity effects and material properties degradation due to the damage initiation and development. The strain-driven implicit integration procedure is developed using equations of continuum damage mechanics, plasticity theory and includes the return mapping algorithm. A tangent operator consistent with the integration procedure is derived to ensure a computational efficiency of the Newton–Raphson method in the finite element analysis. The algorithm is implemented in Abaqus as a user-defined subroutine. The efficiency of the constitutive model and computational procedure is demonstrated using the analysis of the progressive failure of composite laminates containing through holes and subjected to in-plane uniaxial tensile loading. It has been shown that the predicted results agree well with the experimental data reported in the literature.