Viscoelastic Composite Materials Research Articles

Mori-Tanaka Formalism-Based Method Used to Estimate the Viscoelastic Parameters of Laminated Composites.

The paper establishes the mechanical properties of a viscoelastic composite material reinforced with fibers, where the fiber is transverse isotropic and the matrix is isotropic (a common case met in engineering practice). A computation method using the Mori–Tanaka mean field method has been developed in order to apply on viscoelastic materials. Using this procedure, the time-dependent response of a viscoelastic composite material can be determined. Schapery’s nonlinear constitutive equation is also used in the compliance matrix determination of the composite material under investigation. Nonlinearity factors were determined by creep tests at different values of stresses and temperatures and for different materials, based on the least squares method. The results obtained experimentally and their comparison with the theoretically obtained values show a good agreement between experiment and calculation.

Dynamic Response of the Newton Voigt–Kelvin Modelled Linear Viscoelastic Systems at Harmonic Actions

The variety of viscoelastic systems and structures, for the most part, is studied analytically, with significant results. As a result of analytical, numerical and experimental research, which was conducted on a larger variety of linear viscoelastic systems and structures. We analyzed the dynamic behavior for the viscoelastic composite materials, anti-vibration viscous-elastic systems consisting of discrete physical devices, road structures consisting of natural soil structures with mineral aggregates and asphalt mixes, and mixed mechanic systems of insulation of the industrial vibrations consisting of elastic and viscous devices. In this context, the compound rheological model can be schematized as being V−(E|V) type of the Newton Voigt–Kelvin model with inertial excited mass, applicable to linear viscoelastic materials.

On the effective behavior of viscoelastic composites in three dimensions

We address the calculation of the effective properties of non-aging linear viscoelastic composite materials. This is done by solving the microscale periodic local problems obtained via the Asymptotic Homogenization Method (AHM) by means of finite element three-dimensional simulations. The work comprises the investigation of the effective creep and relaxation behavior for a variety of fiber and inclusion reinforced structures (e.g. polymeric matrix composites). As starting point, we consider the elastic-viscoelastic correspondence principle and the Laplace-Carson transform. Then, a classical asymptotic homogenization approach for composites with discontinuous material properties and perfect contact at the interface between the constituents is performed. In particular, we reach to the stress jump conditions from local problems and obtain the corresponding interface loads. Furthermore, we solve numerically the local problems in the Laplace-Carson domain, and compute the effective coefficients. Moreover, the inversion to the original temporal space is also carried out. Finally, we compare our results with those obtained from different homogenization approaches, such as the Finite-Volume Direct Averaging Micromechanics (FVDAM) and the Locally Exact Homogenization Theory (LEHT).

Modeling deformation and failure of viscoelastic composites at finite strains

A micromechanical analysis is proposed for the establishment of the macroscopic constitutive relations for viscoelastic composite materials undergoing large deformations. The composites are assumed to possess a triply periodic microstructure and their viscoelastic constituents are modeled by the incorporation of the viscoelastic effects with an arbitrary chosen hyperelastic strain energy function. Furthermore, an energy limiter is introduced which enforces the saturation of the viscoelastic strain energy function. The value of the strain energy at the saturation corresponds to the failure energy of the viscoelastic constituent. In conjunction with the derived micromechanical analysis, the occurrence of the energy saturation of the viscoelastic constituent predicts the composite failure. Applications are given for the determination of the macroscopic (overall) response and creep of a viscoelastic unidirectional composite, and the behavior of viscoelastic porous materials. In all cases, failure occurrences of the unidirectional composite and porous materials are predicted.

Fuzzy estimates of resonance frequencies for three-layer composite cylindrical panels in smart aerospace and industrial structures

Is developed a numerical-analytical fuzzy-sets methodic for a analysis of the uncertain endogenous parameters of the resonant frequencies in a theoretical model of vibration of thin orthotropic composite three-layer cylindrical panels with small curvature having of symmetrical structure with two external transversally-isotropic piezoelectric layers and with internal orthotropic layer from linearly viscoelastic composite material if available of scatter errors in values of their structural exogenous physical-mechanical and geometric parameters. The technique is based on the transition to fuzzy-interval arguments in the analytical representations for the studied resonant frequencies and in the application of the heuristic principle of generalization to obtain of estimates for the values of such resonant frequencies in the form of normal fuzzy sets. An example of the implementation of the technique under consideration is presented.

Investigation of fracture behavior of asphalt mixture composite using energy-based approach

This study aims to determine the endurance limit and macro-cracking threshold of a viscoelastic composite material using a fracture mechanics approach. Asphalt mixtures containing different recycled material contents and recycling agent doses were fabricated and long-term oven aged. Dynamic modulus tests were first conducted to obtain linear viscoelastic properties including complex modulus and phase angle, and then damage properties were determined from monotonic semi-circular bending tests. Pseudo displacement was calculated to remove the viscous effect from the total dissipated energy, and the energy balance approach and Griffith crack growth criterion were modified and used to predict the bond energy with the aid of discrete element modeling. With the bond energy computed, the endurance limit was determined to be frequency and mixture composition dependent. The macro-cracking threshold defined as the boundary between healable micro-cracks and non-healable macro-cracks was also identified to be frequency and composition dependent using a damage density concept. Both the endurance limit and the macro-cracking threshold were utilized in the asphalt mixture Black Space diagram, which is capable of illustrating the effects of aging, recycled materials content and recycling agent dose in asphalt mixtures for the prediction of fracture performance.

Analysis of bending vibration characteristics of rotating composite boring bar

In this study, the dynamic characteristics of composite boring bar are theoretically investigated. The structural dynamic model of composite boring bar having clamped-free supports is developed by employing Bernoulli-Euler beam theory and considering dissipative characteristics of viscoelastic composite material. The Galerkin method is used to solve the equations of bending vibration. The complex characteristic equation for bending vibration is derived. Numerical examples present the variation of the natural frequency, damping and dynamic stiffness with ply angle, and the variation of the natural frequency and damping with rotating speed are also obtained. The study results show that ply angle, stacking sequences and ratio of length over outer radius have significant influence on the dynamic characteristics of composite boring bar. Conclusively, lamination design can significantly improve dynamic performance and enhance chatter stability in machining.

An approach for modeling non-ageing linear viscoelastic composites with general periodicity

The present work deals with the modeling of non-ageing linear viscoelastic composite materials and quasi-periodic microstructure. The stratified functions and the curvilinear coordinates play an important role in the design of different geometrical shapes. The main objective focuses on the application of two-scales Asymptotic Homogenization Method (AHM) to obtain the overall behavior of the viscoelastic composite materials. Although the whole process is based on the analysis of laminated configurations, a multi-step homogenization scheme to estimate the effective properties of a structure reinforced with long rectangular fibers and wavy effects is used. The associated local problems, the homogenized problem and the analytical expressions for the effective coefficients are obtained by using the correspondence principle and the Laplace-Carson transform. Also, the interconnection between the effective relaxation modulus and the effective creep compliance is performed. Finally, the inversion to the original temporal space is calculated. Some comparisons between the proposed approach and Finite Elements Method (FEM) results are displayed.

Modulus Predicting of Viscoelastic Composite Material and Numerical Method of Inverse Laplace Transform

It is studied about the modulus prediction of viscoelastic composite material and numerical method of inverse Laplace transform. According to elastic-viscoelastic correspondence principle, using Laplace transform, the effective modulus of composite materials is achieved by M-T method in the image domain. Then using inverse Laplace transform, the variation rule of modulus with the time and inclusion fraction would be obtained in the time domain.

The effect of meso-structure and surface topography on the indentation variability of viscoelastic composite materials

Most viscoelastic composites such as biomaterial, polymeric materials and silicone rubber consist of the viscoelastic matrix and the elastic inhomogeneities. Mechanical characterization of the viscoelastic composites helps us to better understand their responses under mechanical stimulation, or improve the design and manufacturing of composite products. The indentation test is the main method for measuring the mechanical properties of viscoelastic composites at present. However, the response of indentation test is sensitive to the microstructural of composites. What’s more, the surface topography also has great influence on the indentation response that cannot be ignored. In this paper, a semi-analytical method is used to model the indentation test in order to explain and improve the indentation test results. The correlation between matrix and inhomogeneity is built by the equivalent inclusion method. The conjugate gradient method and the fast Fourier transform are used to accelerate the solution of unknown variables. Based on the developed model, the effect of micro structure and surface topography on the indentation creep is investigated. The conclusions obtained from the indentation simulation agree well with the experimental results in literatures and provide solid theoretical explanation for the scatter in experimental results.

The energy-based method for effective dynamic properties of viscoelastic composite

Abstract The evolution of viscoelastic composite materials and their practical applications, necessitates the accurate modeling of their viscoelastic characteristics, for which the correspondence principle and energy method are widely used. The energy method for viscoelastic composite materials assumes the zero phase difference among the components of strain at a point, which may affect the accurate prediction of loss factor for high damping composite materials where the phase differences are significant. This work is to present re-formulation of energy method considering these phase differences and to extend it for the computation of effective properties of viscoelastic composites. The computed properties using Finite element method (FEM) with present formulation are observed to be more accurate than the earlier energy formulation with respect to correspondence principle.

Study of the mechanical behavior of asphalt mixtures using fractional rheology to model their viscoelasticity

This study focuses on the mechanical behavior of asphalt mixtures composed of aggregate particles attached with an asphalt binder. Asphalt mixtures are viscoelastic composite materials widely used in the construction of pavement layers. The modelling of such materials is currently done using the Burgers model. However, this model is limited when explaining some of the viscoelastic phenomena of an asphalt mixture, mainly because the Burgers model was developed for a single material with a dual nature. This work presents a new approach that provides a more appropriate framework for studying asphalt mixtures. The model assumes an aggregate particle enclosed by an asphalt material. Viscoelastic equations were developed using derivatives of fractional order. Then, the creep, recovery, and relaxation phenomena in an asphalt mixture were analyzed using the new model. Unlike the Burgers model, the new model can predict the elastic jump observed at the beginning of the creep modulus. Thus, the new model seems to describe better those practical cases of asphalt mixtures used in the construction of pavement layers. The new model can be used to modify the properties of the binder for designing optimized and more resistant asphalt mixtures.

Shear Modulus of a Fiber Composite with a Transtropic Viscolelastic Matrix and Transtropic Elastic Fiber

When solving the problems of deformation solid mechanics, the inhomogeneous composite material is modeled as homogeneous, with averaged mechanical properties − effective characteristics. The purpose of this paper is to develop a technique for determining the effective shear modulus for a viscoelastic fiber composite with a transtropic matrix and fiber. Their isotropy planes coincide and are perpendicular to the fiber axis. The effective shear modulus is defined as a function of the matrix and fiber mechanical properties and the volume content of each of them in a composite. A unidirectional composite material with a hexagonal fiber stacking scheme and a unit cell consisting of a viscoelastic matrix and elastic fiber is considered. The geometric model of a composite is a combination of two coaxial infinite cylinders: a hollow cylinder, modeling the matrix, and a solid one, modeling the fiber inserted into it. The volume of the hexagonal cell is approximated by the volume of the cylinder. The radius of the cylinder is chosen so that the fiber volume content in the hexagonal cell coincides with the value of this characteristic for the cylindrical cell. To describe the viscoelastic properties of a composite, the ratios of the hereditary Boltzmann-Volterra theory are used. The shear modulus is defined as an integral operator with a difference kernel. Two boundary problems are considered: with regard to the longitudinal shear of a transonic viscoelastic solid cylinder modeling the composite, and the joint longitudinal shear of the hollow and solid cylinders that model the matrix and fiber materials, respectively. It is assumed that the displacements and tangential stresses on the contact surface of the matrix and fiber are continuous. A tangential harmonic load is applied on the outer surface of the cylindrical cell. To solve such problems, the Laplace transform is used. As the matching condition, the equality of displacements on the outer surface of the cylinder is used for the two problems. The application of the proposed technique makes it possible to determine the characteristics of the integral operator describing the shear modulus for a viscoelastic composite material. An instantaneous shear modulus and relaxation core parameters are found as the functions of the known mechanical characteristics of the matrix and fiber. As an example, the characteristics of the shear modulus for a composite material consisting of a rubber matrix and polyamide fiber are determined.

Topology optimization of viscoelastic materials on damping and frequency of macrostructures

Damping and natural frequency are the most important characteristics for evaluating the performance of dynamic structures. This paper proposes a topology optimization algorithm based on the bi-directional evolutionary structural optimization (BESO) method to designing viscoelastic materials. This algorithm optimizes damping and natural frequency of macrostructures by tailoring microstructures of viscoelastic materials. The material microstructures are assumed to be composed of periodic unit cells (PUCs) and the effective properties of the PUC are extracted by the homogenization theory and further integrated into the analysis of the macroscopic structure. To improve the performance of dynamic structures, the inverse homogenization is conducted to seek the best distribution of the base materials within the PUC. Numerical examples are presented to demonstrate the effectiveness of the proposed algorithm, which optimizes the microstructures of viscoelastic cellular or composite materials for 2D and 3D structures.

A Comparison Review on Orthopedic Surgery Using Piezosurgery and Conventional Tools

The removal process of hard bone tissue, an anisotropic viscoelastic composite material, during orthopedic surgery, is complicated and challenged. Piezosurgery has been applied increasingly in orthopedic surgery because of its selective cutting attribute and much more precision compared to conventional tools. However, whether it can solve the problems of cutting hard bone tissue remains unknown. This paper reviews the mechanism of piezosurgery, analyses the advantages and disadvantages of piezosurgery and conventional tools during hard bone tissue cutting from different aspects, such as cutting force, cutting temperature, tissue damage, cutting efficiency, etc. Some directions for further research are also highlighted.

A design of active constrained layer damping treatment for vibration control of circular cylindrical shell structure

A new 1-3 viscoelastic composite material (VECM) layer is designed for improved active constrained layer damping (ACLD) treatment of vibration of a functionally graded (FG) circular cylindrical shell. Besides this improved active damping treatment, another objective of this study is to control all the modes of vibration of the shell effectively using the treatment (active constrained layer damping) in layer-form throughout the outer shell-surface. In this design of active constrained layer damping treatment in layer-form, its (active constrained layer damping) necessary conformability with the curved host shell-surface is ensured by the use of a vertically reinforced 1-3 piezoelectric composite (PZC) constraining layer, whereas the effective control of several modes of vibration of the shell is achieved by the use of electrode-patches over the surfaces of the constraining layer. A fruitful strategy in the arrangement of electrode-patches is proposed for effective control of several modes of vibration of the shell using one configuration of the electrode-patches. An electric potential function is assumed for this use of electrode-patches and a geometrically nonlinear coupled electro-visco-elastic incremental finite element model of the overall shell is developed for its analysis in the frequency-domain. The analysis reveals significant improvement of active damping characteristics of the active constrained layer damping layer for the use of the present 1-3 viscoelastic composite material layer instead of the traditional monolithic viscoelastic material (VEM) layer. The analysis also reveals the suitability of the present strategy of arrangement of electrode-patches for achieving aforesaid control-activity of the ACLD layer. The effects of temperature in the host functionally graded shell and different geometric parameters in the design of the 1-3 viscoelastic composite material layer on the damping characteristics of overall shell are also presented.

Hydrodynamic description of elastic or viscoelastic composite materials: Relative strains as macroscopic variables.

One possibility to adjust material properties to a specific need is to embed units of one substance into a matrix of another substance. Even materials that are readily tunable during operation can be generated in this way. In (visco)elastic substances, both the matrix material as well as the inclusions and/or their immediate environment can be dynamically deformed. If the typical dynamic response time of the inclusions and their surroundings approach the macroscopic response time, their deformation processes need to be included into a dynamic macroscopic characterization. Along these lines, we present a hydrodynamic description of (visco)elastic composite materials. For this purpose, additional strain variables reflect the state of the inclusions and their immediate environment. These additional strain variables in general are not set by a coarse-grained macroscopic displacement field. Apart from that, during our derivation, we also include the macroscopic variables of relative translations and relative rotations that were previously introduced in different contexts. As a central point, our approach reveals and classifies the importance of a macroscopic variable termed relative strains. We analyze two simplified minimal example geometries as an illustration.

Laser-Generated Lamb Waves Propagation in Multilayered Plates Composed of Viscoelastic Fiber-reinforced Composite Materials

The propagation characteristics of laser-generated Lamb waves in multilayered fiber-reinforced composite plates with different fiber orientations and number of layers have been investigated quantitatively. Considering the viscoelasticity of the composite materials, we have set up finite element models for simulating the laser-generated Lamb waves in two types of the multilayered composite plates. In the first type, different fiber orientations are adopted. In the second one, different number of layers are considered. The results illustrate the occurrence of attenuation and dispersion, which is induced by the viscoelasticity and multilayer structure, respectively.

Modal testing of nanocomposite materials through an optimization algorithm

An efficient identification method for modal testing of viscoelastic composite materials is demonstrated in this paper, through the analytical–experimental transfer function method. The procedure for the identification of analytical–experimental transfer functions is carried out using a genetic algorithm (GA) by minimizing the difference between the measured response from tests and the calculated response, which is a function of the modal parameters. The analytical transfer functions provide a sub-structuring process to identify modes, as a function of damped natural frequencies and loss factors of a complex structure and it is insensitive to experimental noise as well as the modal coupling effect. The proposed method is verified with the calculation of the elastic modulus and modal properties of a cantilever steel beam with the FEM and compared with the identification results of the proposed algorithm. The effectiveness of the proposed method is demonstrated by investigating the static and dynamic behavior of epoxy cantilever beam specimens reinforced with silica nanoparticles. Analytical–experimental transfer functions accurately identified the viscoelastic and dynamic response of the studied specimens, while the results indicated that the inclusion of nanosilica particles increased the stiffness of the epoxy network and the damping response of the reinforced specimens is improved.

An approximate multiscale model for aging viscoelastic materials exhibiting time-dependent Poisson's ratio

A multi-scale homogenization scheme is proposed to estimate the time-dependent strains of fiber-reinforced concrete. This material is modeled as an aging linear viscoelastic composite material featuring ellipsoidal inclusions embedded in a viscoelastic cementitious matrix characterized by a time-dependent Poisson's ratio. To this end, the homogenization scheme proposed in Lavergne et al. [1] is adapted to the case of a time-dependent Poisson's ratio and it is successfully validated on a non-aging material computed in the Fourier domain. Finally, the new extended estimates of the time-dependent strains of fiber-reinforced concrete are compared to the experimental measurements of Chern and Young [2] and the effects of the volume fraction and aspect ratio of the steel fibers on the time-dependent strains of fiber-reinforced concrete are investigated.