Viscoelastic Interlayer Research Articles

Wide Scale Characterization and Modeling of the Vibration and Damping Behavior of CFRP-Elastomer-Metal Laminates\u2014Comparison and Discussion of Different Test Setups

The investigated hybrid carbon fiber reinforced plastics-elastomer-metal laminates (HyCEML) offer the potential of tailored structural materials with adaptable damping properties. Conventional fiber metal laminates, like glass laminate aluminum reinforced epoxy are already widely spread in the aviation industry owing to their outstanding fatigue behavior. By integrating an elastomeric interlayer, the glass fibers can be substituted by carbon fibers and damping properties of these laminates can be adjusted. The viscoelastic interlayer dissipates energy within the laminate by inducing shear strain during bending, which is commonly known as constrained layer damping. The aim of this paper is the description of the vibration and damping behavior of HyCEML over a wide temperature and frequency range by using different test methods. Dynamic mechanical analysis is used for the individual polymeric constituents and coupon specimens and modal analysis is used with different specimen geometries up to a component sized panel. In addition, analytical and numerical approaches complement the experiments and lead to a deeper understanding of the vibration and damping behavior. Owing to the high damping, already at frequencies of 5 kHz only running waves can be detected for the investigated panel size. The discussion of different test methods helps to identify material and wavelength dependent effects, but also possible adverse effects of certain methods.

Finite element modeling of the joint action of flow slide and protective structure

Introduction. In the context of the problem of plane deformation, a finite-element model of a natural landslide slope is developed. It allows for the joint work of a flow slide and a protective engineering structure. The Drucker-Prager model is used to take into account the physical nonlinearity of the slope layer material. To activate the kinematic instability, a viscoelastic interlayer is introduced into the design scheme, along which the landslide layer slides. Materials and Methods. Numerical experiments were performed using the ANSYS Mechanical software package, which implements the finite element method in the form of the displacement method. Slope discretization is performed on the basis of PLANE42 flat four-node finite elements. To simulate the displacement of the landslide layer relative to the fixed base, the combined viscoelastic elements COMBIN14 were used. Results. A physically nonlinear model of a natural landslide slope consisting of a base, a landslide layer, and a viscoelastic interlayer, is formalized. An engineering technique for analyzing the stress-strain state of the “slopeprotective structure” system has been developed, taking into account the kinematic instability of the landslide layer. A series of computational experiments was carried out. Discussion and Conclusion. Based on the calculations performed, it is shown that the proposed method enables to specify the force action of the landslide layer on the protective structure and, thereby, to increase the reliability of the risk assessment when activating the landslide process.

3D analytical solution for multilayer functionally graded plates with viscoelastic interlayers

In this study, an analytical model is developed to research on the time-varying performance of multilayer functionally graded plates glued by viscoelastic interlayers. In the plate, the elastic modulus in each graded layer is exponentially distributed along the thickness, and its mechanical property is modeled on the basis of the three-dimensional (3D) elasticity theory. The viscoelastic property in the interlayer is described by the standard linear solid model considering hereditary nature of viscoelasticity. By using the series expansion and the Laplace transformation, the solutions of stress and displacement for the multilayer plate are analytically derived out. The comparison analysis indicates that the finite element solution and the present one have a good agreement. The Kirchhoff-Love solution becomes imprecise as the thickness or the gradient index increases, because the transverse shear deformation is ignored. In the parameter analysis, the effects of the time variable, the gradient index and the viscoelastic constants on the time-varying performance of the multilayer functionally graded plate are analyzed in detail. The results show that the stress and displacement distributions of the multilayer functionally graded plate can be optimized by changing the gradient index.

State-space method for dynamic responses of double beams with general viscoelastic interlayer

Due to their effective engineering applications, double-beam systems have intensively been studied in recent decades. The interlayer between beams in the system plays a key role in the structural vibration and energy dissipation. However, existing research efforts only observe the pure elastic interlayer or simplest viscoelastic interlayer such as Kelvin-model interlayer. In this paper, a general viscoelastic interlayer that can consider more complex stiffness and damping effects is investigated. A novel state-space approach with the proposed mode-shape constant is presented to determine the transverse vibration of the double-beams. The given integrals of mode shapes can effectively decouple the governing equations, making it possible to analyze the complex viscoelastic interlayer. Numerical examples demonstrate that the proposed method is accurate and reliable. The viscoelastic interlayer affects the natural frequencies of asynchronous vibration mode more apparently than those of synchronous vibration mode. The damping coefficients of the viscoelastic interlayer have a significant effect on the damping characteristic of the double-beam systems while reducing the dynamic responses of the beams in the forced vibration. The proposed method can be useful to simulate the dynamic responses of double-beam systems with various viscoelastic interlayers in engineering practices and applications.

Extension of an analytical solution of a unified formulation to the frequency response of composite plates with viscoelastic layers

AbstractResulting from their high stiffness and low weight, lightweight structures made from fiber reinforced polymers are usually prone to vibrations. The inclusion of viscoelastic interlayers can provide a viable mean to passively damp these structures due to constrained layer damping. For the modeling of such structures, a layerwise approach based on the Generalized Unified Formulation has previously been proven suitable for static load cases.This contribution presents an analytical procedure to determine the frequency response and vibration characteristics of such heterogeneous laminates incorporating viscoelastic layers. Specifically, simply supported plates modeled by the Generalized Unified Formulation are considered and solved using Navier type solutions. The approach is validated by comparison with 3D finite element models. Particular focus is put on the order of expansion in thickness direction needed to accurately predict the frequency response of the laminate.

Time-dependent characteristics of two-layer functionally graded plates adhesively bonded by a viscoelastic interlayer based on Kirchhoff plate theory

An analytical solution is proposed to investigate the time-dependent characteristics of two-layer functionally graded plates with a viscoelastic interlayer. The elastic modulus in each graded layer varies through the thickness following an arbitrary function, and its mechanical properties are described based on the Kirchhoff theory. The Maxwell-Wiechert model is applied to simulate the viscoelastic adhesive interlayer with the neglect of memory effect. The energy equation of the system is expressed by the deformation components, which are expanded as the double trigonometric series. By virtue of variational method, the solutions of stress and deformation are determined efficiently. The comparison study indicates that the present solution matches the finite element solution well; however, the finite element method is highly time-consuming because of the fine mesh in the geometric shape and the time step. Finally, the influences of the geometry and material on the time-dependent behavior of the structure are discussed in detail.

High strain-rate effects from blast loads on laminated glass: An experimental investigation of the post-fracture bending moment capacity based on time–temperature mapping of interlayer yield stress

To enhance the resilience of buildings, laminated glass panels are increasingly used in glazed façades. These ductile panels provide a superior blast resistance to that provided by monolithic glass panels, due to the improved residual capacity offered by the polymer interlayer following the fracture of the glass layers. The complex interaction between the attached glass fragments and the interlayer is still only partially understood. To help address this, this paper investigates experimentally the post-fracture bending moment capacity of laminated glass. Three-point bending tests are performed at low temperature on specimens pre-fractured before testing, to ensure controlled and repeatable fracture patterns. The low temperature simulates the effects of the high strain-rates that result from short-duration blast loads by taking advantage of the time–temperature dependency of the viscoelastic interlayer. In these experiments, polyvinyl butyral is considered as the interlayer, this being the most common interlayer for laminated glass used in building facades. A new time–temperature mapping equation is derived from experimental results available in the literature, to relate the temperatures and strain-rates that result in the same interlayer yield stress. The results of the low-temperature tests demonstrate an enhancement of the ultimate load capacity of the fractured glass by two orders of magnitude, compared to that at room temperature. This suggests an improved post-fracture bending moment capacity associated with the now stiffer interlayer working in tension and the glass fragments working in compression. Due to the time–temperature dependency of the interlayer, a similar enhancement is therefore anticipated at the high strain-rates associated with typical blast loading. Finally, the assumed composite bending action is further supported by the results from additional specimens with thicker PVB and glass layers, which result in enhanced capacity consistent with the bending theory of existing analytical models.

Exact solution for infinite multilayer pipe bonded by viscoelastic adhesive under non-uniform load

An analytical solution is presented for an infinite multilayer pipe bonded by viscoelastic interlayer subjected to racial loads non-uniformly distributed along the circumferential direction in order to investigate its time-dependent behavior. The elasticity equations in the polar coordinate are used to describe the stresses and displacements in each pipe layer. The viscoelastic property of the interlayer is modeled by the standard linear solid model considering the strain memory effect. By means of the Fourier series expansion method, the general solution of stresses and displacements is derived out with unknown coefficients, which are further determined by using the analytical Laplace transformation method. The present solution obtained can be used as the benchmark to validate other solutions such as finite element solution for the same problem. The comparison study shows a trend of the finite element solution converging to the present one as the mesh becomes refined; however, such a finite element model is time-consuming. The influences of load distribution, geometry and material parameters on the time-dependent stress and displacement fields in the pipe are discussed detailedly.

Adhesion rupture in laminated glass: influence of adhesion on the energy dissipation mechanisms

When laminated glass shatters under impact, most of the energy dissipation occurs in the coupled delamination and stretching of the polymer interlayer between broken chunks of glass. The strong dependency of these mechanisms on interlayer nature, on loading rate and on temperature has been previously investigated: however, the effect of the interfacial adhesion is unexplored. In this work, a surface modification technique is proposed, along with a mechanical characterization of the debonding with the Through Crack Tensile Test. We show that while increasing adhesion has the effect of enhancing the energy required to propagate the delamination fronts as well as the stretch level of the delaminated interlayer, the dissipation associated to the stretching of the volume of the PVB interlayer seems unaffected. We attribute this effect to the competition between the changes in both stretch and stretch rate in the viscoelastic interlayer. Finally, we discuss the experimental observation of the limits of the steady-state debonding regime, related to the competition between adhesive crack propagation and cohesive failure in the interlayer.

Analytical Solutions for Functionally Graded Sandwich Plates Bonded by Viscoelastic Interlayer Based on Kirchhoff Plate Theory

In this paper, an analytical solution for functionally graded sandwich plate adhesively bonded by viscoelastic interlayer is proposed to research its time-dependent behavior. The Kirchhoff plate theory is employed to describe the mechanical property of each gradient layer with elastic modulus defined as the arbitrary function through the thickness direction. The standard linear solid model is applied to simulate the viscoelasticity of the interlayer with considering the strain memory effect. By the use of the vibrational method and the Laplace transformation, the solutions of stresses and displacements are solved analytically. The validation study indicates that the present solution is correct and more effective than the finite element solution because of the fine mesh both in the geometric shape and the time step. In addition, the influences of the geometry and material parameters on the time-dependent behavior of the sandwich plate are investigated in detail.

Exact solutions for multilayer functionally graded beams bonded by viscoelastic interlayer considering memory effect

This work proposes exact solutions for simply supported multilayer functionally graded (FG) beams with viscoelastic interlayer to predict its time-dependent mechanical behavior. The stresses and deformations of FG layers are described by the two-dimensional (2-D) elasticity theory. The viscoelastic property of the interlayer is simulated by the standard linear solid model, and its constitutive relation is expressed in the convolution form which considers the strain memory effect. The general solutions of FG layers involving undetermined coefficients are obtained by virtue of the Fourier series expansion. By the use of the Laplace transform method, the solutions of stresses and deformations are determined analytically. The present solutions including Fourier series possess good convergence property. The comparison studies indicate that the finite element (FE) solutions approach the present ones when each FG layer is divided into many isotropic sub-layers in FE model and the gradient factor is taken as small value. The relative error of the one-dimensional (1-D) Euler-Bernoulli solutions is slight for slender beam with small gradient factor, but it significantly increases as the beam thickness or the gradient factor grows. Finally, the influences of the material constants on the time-dependent behavior in the beam are investigated in detail.

Time-dependent behavior of laminated functionally graded beams bonded by viscoelastic interlayer based on the elasticity theory

A two-dimensional (2-D) elasticity solution is developed to investigate the time-dependent response of laminated functionally graded beam with viscoelastic interlayer. The elastic modulus in each functionally graded layer varies through the thickness following an exponential function, and the mechanical property of each layer is described by the exact 2-D elasticity equations. Viscoelastic property in the interlayer is simulated by the Maxwell–Wiechert model, in which the memory effect of it is neglected. By virtue of the recursive matrix method, the solution of stress and deformation can be obtained efficiently. The comparison studies indicate that the relative error of the Euler–Bernoulli solution is slight for slender beam with small gradient factor, but it significantly increases as the beam thickness or the gradient factor grows. The finite element solution is close to the present one with large number of sub-layers in FE modeling and small gradient factor of FG layer, while the error of FE solution increases as the number of sub-layers decrease or the gradient factor increases. Besides, the influences of material parameters upon the time-dependent behavior and the optimization for the stress and deformation in the beam are discussed in detail.

Issues on the Vibration Analysis of In-Service Laminated Glass Structures: Analytical, Experimental and Numerical Investigations on Delaminated Beams

Load-bearing laminated glass (LG) elements take the form of simple members in buildings (i.e., columns, beams, and plates) or realize stand-alone assemblies, where glass and other traditional constructional materials can interact. Among several relevant aspects, the dynamic response of LG structures requires dedicated methods of analysis, towards the fulfilment of safe design purposes. A combination of multiple aspects must be taken into account for dynamic calculations of even simple LG elements when compared to static conditions, first of all the sensitivity of common interlayers to the imposed vibration frequency. The challenge is even more complex for the vibration serviceability assessment of in-service LG structures, where the degradation of materials and possible delamination effects could manifest, hence resulting in structural performances that can markedly differ from early-design conditions. Major uncertainties can be associated to the actual mechanical characterization of materials in use (especially the viscoelastic interlayers), as well as the contribution of restraints (as compared to ideal boundaries) and the possible degradation of the bonding layers (i.e., delaminations). All of these aspects are examined in the paper, with the support of extended analytical calculations, on-site experimental measurements, and parametric Finite Element (FE) numerical analyses. When compared to literature efforts accounting for ideal boundaries only, an analytical formulation is proposed to include the effects of flexible restraints in the dynamic performance of general (double) LG beams. Special care is also spent for the presence of possible delaminations, including size and position effects. In the latter case, existing formulations for composite laminates are preliminarily adapted to LG beams. Their reliability and accuracy is assessed with the support of test predictions and parametric FE simulations.

Static and dynamic effective thickness in five-layered glass plates

In the last years, the effective thickness concept has been used to calculate deflections, stresses and modal parameters in laminated glass beams and plates, which consists of using a monolithic element with equivalent bending properties to a laminated element, i.e. the thickness of the equivalent monolithic model is time and temperature dependent because the interlayers show a viscoelastic behavior. Multi-layered laminated glass panels are those with at least three monolithic glass layers and two viscoelastic interlayers which are commonly used in floors, roofs and other applications where a high level of security is required. In this paper, a static deflection effective stiffness for a laminated glass plate consisting of three glass layers and two polymeric interlayers is derived. This static effective thickness is then extended to the frequency domain using the correspondence principle. The models are validated by static experimental tests and operational modal tests carried out on a rectangular multi-layered laminated glass plate pinned supported at the four corners.

Analytical Solution of Deformations for Two‐Layer Timoshenko Beams Glued by a Viscoelastic Interlayer

An analytical solution of stresses and deformations for two‐layer Timoshenko beams glued by a viscoelastic interlayer under uniform transverse load is presented. The standard linear solid model is employed to simulate the viscoelastic characteristics of the interlayer, in which the memory effect of strains is considered. The mechanical behavior of each layer is described by the first‐order shear deformation theory (FSDT). By means of the principle of minimum potential energy, a group of equations for displacements and rotation angles are derived out. The final solution is obtained by conducting the Laplace transform and the inversion of Laplace transform to the equation group. Numerical comparison shows that the present solutions and the finite element results are in good agreement. It is shown that the present results are more accurate than those obtained from the Euler‐Bernoulli beam theory, especially for thick beams. And the present solutions can accurately describe the variation of stresses and deformations of the beam with the time, compared with those ignoring the memory effect of strains. Finally, the effects of the geometric parameters and material properties of the interlayer on stresses and deformations of the beam are studied in detail.

Benchmark solution for multilayer magneto-electro-elastic plates adhesively bonded by viscoelastic interlayer

An analytical solution is developed for a simply supported multilayer magneto-electro-elastic plate, which is adhesively bonded by viscoelastic interlayer and subjected to transverse loading. The three-dimensional equations of magneto-electro-elasticity are used to describe the mechanical behavior in each layer of the plate, while the mechanical property of the viscoelastic interlayer is simulated by the standard linear solid model with strain memory effect. The imperfect electric conditions between adjacent layers are considered. Making use of the Fourier series expansion as well as the state-space method, a linear equation system to the solution of the problem considered is derived. By means of the Laplace transformation, the undetermined coefficients contained in the equation system are obtained analytically. The present solution can be used as the benchmark to assess the other numerical solutions. The comparison study shows a trend that the finite element solution converges to the proposed theoretical results as the mesh density increases; in contrast to the theoretical solution, the finite element solution is, however, time-consuming, in terms of mesh division and calculation. In this study, the effects of the time; interlayer thickness; and interlayer electric coefficient on the mechanical, electric, and magnetic fields are also investigated.

Applications of finite element modelling in failure analysis of laminated glass composites: A review

Abstract The subject of the paper is modelling of complex damage behaviour of laminated glass, which is a sandwiched polymer composite. Last 20 years have witnessed extensive growth in computational modelling of complex nonlinear behaviour of laminated glass panels with viscoelastic interlayers. Present review article is an attempt to highlight applications of finite element approach in failure analysis of laminated glasses. Evolution of modelling theories such as equivalent single layer theories, layerwise theories and zig-zag models have been presented to insight the fundamental concepts used in modelling. Finite element techniques such as erosion, cohesive zone and extended finite element methods available in FE packages are briefly reviewed alongwith material models for glass and interlayer. The systematic growth in FE models in numerical simulation of human head impact on windshields and blast loading is specifically presented. Finite element models have been proposed as useful guides to engineers for fabrication of laminated glasses with more realistic data to be used in real world situations without going for expensive and time consuming experimental set ups. Overall 223 research articles have been included exhibiting the research performed in context of laminated glass.

Numerical Analysis and 1D/2D Sensitivity Study for Monolithic and Laminated Structural Glass Elements under Thermal Exposure.

Glass is largely used in architectural and engineering applications (i.e., buildings and vehicles) as a structural material, especially in the form of laminated glass (LG) sections. To achieve adequate and controlled safety levels in these applications, the well-known temperature-dependent behavior of viscoelastic interlayers for LG sections should be properly accounted for during the design process. Furthermore, the materials’ thermomechanical degradation with increases of temperature could severely affect the load-bearing performance of glass assemblies. In this context, uncoupled thermomechanical finite element (FE) numerical models could represent a robust tool and support for design engineers. Key input parameters and possible limits of the FE method, however, should be properly calibrated and assessed, so as to enable reliable estimations for the real behavior of glazing systems. In this paper, FE simulations are proposed for monolithic (MG) and LG specimens under radiant heating, based on one-dimensional (1D) and two-dimensional (2D) models. A special attention is focused on thermal effects, being representative of the first step for conventional uncoupled, thermomechanical analyses. Based on experimental results available in the literature, FE parametric studies are discussed, giving evidence of limits and issues due to several modeling assumptions. In particular, careful consideration is paid for various thermal material properties (conductivity, specific heat) and thermal boundaries (conductivity, emissivity), but also for other influencing parameters like the geometrical features of samples (thickness tolerances, cross-sectional properties, etc.), the composition of LG sections (interlayer type, thickness), the loading pattern (heat transfer distribution) and the presence of additional mechanical restraints (i.e., supports of different materials). Comparative FE results are hence critically discussed, highlighting the major effects of such influencing parameters.

Time-dependent behavior of layered magneto-electro-elastic cylindrical shell with viscoelastic interlayer

In this work, an analytical solution for layered magneto-electro-elastic (MEE) cylindrical shell adhesively bonded by viscoelastic interlayer is developed to predict its time-dependent mechanical, electric and magnetic behaviors. The viscoelastic characteristic of the interlayer is modelled by the standard linear solid model. Each MEE layer is governed by the equations of magneto-electro-elasticity. The imperfect electric conditions between adjacent MEE layers are also considered. Using the Pseudo-Stroh formalism, a general solution with unknown coefficients is derived for each MEE layer. The Laplace transformation is applied to the constitutive equations of the viscoelastic interlayer. The coefficients are determined by the surface conditions as well as the interface conditions. The present solution can be used as the benchmark to assess results from numerical approaches. It is shown that the finite element solution converges to the present one as the mesh density increases; however, the finite element method is time-consuming in mesh division and calculation. Finally, the effects of time, shell angle, interlayer thickness and imperfect electric coefficient on the mechanical, electric and magnetic behaviors are investigated.

Numerical modeling of sound and vibration reduction using viscoelastic materials and shunted piezoelectric patches

In this paper, a reduced order coupled finite element/boundary element method (FEM/BEM) for control of noise radiation and sound transmission of vibrating structure by viscoelastic and passive piezoelectric treatments is presented. The system consists of a sandwich structure composed of elastic faces and a viscoelastic core (with surface mounted piezoelectric patches) and coupled to external/internal acoustic domains. The passive shunt damping strategy is employed for vibration attenuation in the low-frequency range while dissipative viscoelastic materials are used for the higher-frequency domain. The originality of the present paper lies (i) in evaluating the classically used FEM/BEM methods for structural-acoustics problems when taking account smart systems at the fluid-structure interfaces and viscoelastic interlayers and (ii) in development of a reduced-order model, based on a normal mode expansion, able to capture the main characteristics of the system dynamical behavior.