Viscoelastic Composites Research Articles

The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites

A finite strain micromechanical model is generalized in order to incorporate the effect of evolving damage in the metallic and polymeric phases of unidirectional composites. As a result, it is possible to predict the response of composites with ductile and brittle phases undergoing large coupled inelastic-damage and viscoelastic-damage deformations, respectively. For inelastic composites, both finite strain elastoplastic (time-independent) and viscoplastic (time-dependent) behaviors are considered. The ductile phase exhibits initially a hyperelastic behavior which is followed by an inelastic one, and its analysis is based on the multiplicative split of its deformation gradient into elastic and inelastic parts. The embedded damage mechanisms and their evolutions are based on Gurson’s (which is suitable for the modeling of porous materials) and Lemaitre’s finite strain models. Similarly, the polymeric phase exhibits large viscoelastic deformations in which the damage evolves according to a suitable evolution law that depends on the amount of accumulated deformation. Evolving damage in hyperelastic materials can be analyzed as a special case by neglecting the viscous effects. The micromechanical analysis is based on the homogenization technique for periodic multiphase materials, which establishes the strong form of the Lagrangian equilibrium equations. These equations are implemented together with the interfacial and periodic boundary conditions, in conjunction with the current tangent tensor of the phase. As a result, the instantaneous strain concentration tensor that relates the local deformation gradient of the phase to the externally applied deformation gradient is established. This provides also the instantaneous effective stiffness tangent tensor of the composite as well as its current response. Results are given that exhibit the effect of damage on the initial yield surfaces, response and possible failure of the composite.

Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks

AbstractMultiscale computational techniques play a major role in solving problems related to viscoelastic composites due to the complexities inherent to these materials. In this paper, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local‐scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history‐dependent stress tensor at the global scale depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. The procedure is basically developed by relating the local‐scale displacement field to the global‐scale strain tensor and using first‐order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify the approach and demonstrate the model capabilities. Copyright © 2009 John Wiley & Sons, Ltd.

Deformation in viscoelastic sandwich composites subject to moisture diffusion

This study analyzes the effect of moisture diffusion on the deformation of viscoelastic sandwich composites, which are composed of orthotropic fiber-reinforced laminated skins and viscoelastic polymeric foam core. It is assumed that the elastic and time-dependent (transient) moduli at any particular location in the foam core depend on the moisture concentration at that location. Sequentially coupled analyses of moisture diffusion and deformation are performed to predict overall performance of the studied viscoelastic sandwich systems. Time and moisture dependent constitutive model is used for the polymer foam core, while skins are assumed linear elastic. The overall time-dependent responses of the sandwich composites subject to moisture diffusion are analyzed using finite element (FE) method. Experimental data available in the literature and analytical solutions are used to support convergence studies in the FE analyses. Contributions of moisture dependent elastic and the time-dependent moduli to the overall stress, strain and displacement field are studied. FE analyses of the delamination between skins and core in sandwich composite under combined moisture diffusion and mechanical loading are also performed.

Determination of effective damping characteristics of fiber-reinforced viscoelastic composites

A numerical method for the determination of effective complex moduli and vibration decrements of fiber-reinforced viscoelastic composites is proposed, which is based on the finite element modeling of representative volume element and equation of the elastic and viscous parts of the strain energy of composite and quasi-homogeneous material volumes.

Effective thermal properties of viscoelastic composites having field-dependent constituent properties

This study introduces a micromechanical model for predicting effective thermal properties (linear coefficient of thermal expansion and thermal conductivity) of viscoelastic composites having solid spherical particle reinforcements. A representative volume element (RVE) of the composites is modeled by a single particle embedded in the cubic matrix. Periodic boundary conditions are imposed to the RVE. The micromechanical model consists of four particle and matrix subcells. Micromechanical relations are formulated in terms of incremental average field quantities, i.e., stress, strain, heat flux and temperature gradient, in the subcells. Perfect bonds are assumed along the subcell’s interfaces. Stress and temperature-dependent viscoelastic constitutive models are used for the isotropic constituents in the micromechanical model. Thermal properties of the particle and matrix constituents are temperature dependent. The effective coefficient of thermal expansion is derived by satisfying displacement and traction continuity at the interfaces during thermo-viscoelastic deformations. This formulation leads to an effective time–temperature–stress-dependent coefficient of thermal expansion. The effective thermal conductivity is formulated by imposing heat flux and temperature continuity at the subcells’ interfaces. The effective thermal properties obtained from the micromechanical model are compared with analytical solutions and experimental data available in the literature. Finally, parametric studies are also performed to investigate the effects of nonlinear thermal and mechanical properties of each constituent on the overall thermal properties of the composite.

Multicoating Inhomogeneities Problem for Effective Viscoelastic Properties of Particulate Composite Materials

The present work extends the multicoated micromechanical model of Lipinski et al. (2006, “Micromechanical Modeling of an Arbitrary Ellipsoidal Multi-Coated Inclusion,” Philos. Mag., 86(10), pp. 1305–1326) in the quasistatic domain to compute the effective material moduli of a viscoelastic material containing multicoated spherical inclusions displaying elastic or viscoelastic behavior. Losses are taken into account by introducing the frequency-dependent complex stiffness tensors of the viscoelastic matrix and the multicoated inclusions. The advantage of the micromechanical model is that it is applicable to the case of nonspherical multicoated inclusions embedded in anisotropic materials. The numerical simulations indicate that with proper choice of material properties, it is possible to engineer multiphase polymer system to have a high-loss modulus (good energy dissipation characteristics) for a wide range of frequencies without substantially degrading the stiffness of the composite (storage modulus). The numerical analyses show also that with respect to the relative magnitudes of the loss factors and the storage moduli of the matrix, inclusion and coating, the overall properties of the viscoelastic particulate composite are dominated by the properties of the matrices in some frequency ranges. The model can thus be a suitable tool to explore a wide range of microstructures for the design of materials with high capacity to absorb acoustic and vibrational energies.

Frequency dependent thermal expansion in binary viscoelastic composites

The effective thermal expansion coefficient β ∗ of a binary viscoelastic composite is shown to be frequency dependent even if the thermal expansion coefficients β A and β B of both constituents are themselves frequency independent. Exact calculations for binary viscoelastic systems show that β ∗ is related to constituent values β A , β B , volume fractions, and bulk moduli K A , K B , as well as to the overall bulk modulus K ∗ of the composite system. Then, β ∗ is determined for isotropic systems by first bounding (or measuring) K ∗ . For anisotropic systems with hexagonal symmetry, the principal values of the thermal expansion β ⊥ ∗ and β ∥ ∗ can be determined exactly when the constituents form a layered system. In all the examples studied, it is shown explicitly that the eigenvectors of the thermoviscoelastic system possess non-negative dissipation – despite the complicated analytical behavior of the frequency dependent thermal expansivities themselves. Methods presented have a variety of applications from fluid–fluid mixtures to fluid–solid suspensions, and from fluid-saturated porous media to viscoelastic solid–solid composites.

Dynamic Relaxation Nonlinear Viscoelastic Analysis of Annular Sector Composite Plate

The geometrically nonlinear laminated annular plate structure with nonlinear viscoelastic orthotropic composite is considered using the dynamic relaxation (DR) method for the first time in the present study. The DR technique in conjunction with the finite difference discretization is used to study the behavior of a Mindlin plate. The plate is made of nonlinear viscoelastic orthotropic material expressed by the Schapery single integral model. A recursive-iterative formulation is implemented for the hereditary integral of the material. Under uniform lateral pressure and clamped and hinged edged constraints, the unsymmetrical laminated sector plate deformation is predicted in different times. The present results are compared with the elastic finite element (FE) generated numerical results. The correlations are very satisfactory. The load-center deflections for linear and nonlinear viscoelastic material plate along the symmetrical radial line for elastic and viscoelastic plate are illustrated. The dimensionless deflection results for up to 480min are predicted to show the creep behavior of the material. Finally, the dimensionless stress couple results are obtained after 8 h creep time for a graphite/epoxy composite plate.

A Mixture Theory for Microstretch Thermoviscoelastic Solids

A nonlinear theory is developed for a heat-conducting viscoelastic composite which is modelled as a mixture consisting of a microstretch Kelvin–Voigt material and a microstretch elastic solid. The strain measures, the basic laws and the constitutive equations are established and presented in Lagrangian description. The initial boundary value problem associated to such model is also formulated. Then the linearized theory is considered and the constitutive equations are given for both anisotropic and isotropic bodies. Finally, a uniqueness result is established within the framework of the linear theory.

Responses of viscoelastic polymer composites with temperature and time dependent constituents

This study formulates a concurrent micromechanical model for predicting effective responses of fiber reinforced polymer (FRP) composites, whose constituents exhibit thermo-viscoelastic behaviors. The studied FRP composite consists of orthotropic unidirectional fiber and isotropic matrix. The viscoelastic material properties for the fiber and matrix constituents are allowed to change with the temperature field. The composite microstructures are idealized with periodically distributed square fibers in a matrix medium. A unit-cell model, consisting of four fiber and matrix subcells, is generated to obtain effective nonlinear thermo-viscoelastic responses of the composites. A time-integration algorithm is formulated to link two different thermo-viscoelastic constitutive material models at the lowest level (homogeneous fiber and matrix constituents) to the effective material responses at the macro level, and to transfer external mechanical and thermal stimuli to the constituents. This forms a concurrent micromechanical model, which is needed as the material properties of the constituents depend on the temperature field. Consistent tangent stiffness matrices are formulated at the fiber and matrix constituents and also at the effective composite level to improve prediction accuracy. The thermo-viscoelastic responses obtained from the concurrent micromodel are verified with available experimental data. Detailed finite element (FE) models of the FRP microstructures are also generated using 3D continuum elements for several fiber volume fractions. Thermo-viscoelastic responses of the concurrent micromodel are also compared to the ones of the detailed FRP microstructures.

Homogenization of nonlinear visco-elastic composites

Quasi-static processes in nonlinear visco-elastic materials of solid-type are here represented by the system: (∗) σ − B ( x ) : ∂ ε ∂ t ∈ β ( ε , x ) , − div σ = f → , coupled with initial and boundary conditions. Here σ denotes the stress tensor, ε the linearized strain tensor, B ( x ) the viscosity tensor, β ( ⋅ , x ) a (possibly multi-valued) maximal monotone mapping, and f → an applied load. Existence and uniqueness of the weak solution are proved. A composite material in which the data β and B rapidly oscillate in space is then considered, and a two-scale model is derived via Nguetseng's notion of two-scale convergence. Although neither the stress nor the strain need be mesoscopically uniform, it is proved that their coarse-scale averages solve a global-in-time single-scale homogenized problem ( upscaling). From any solution of the latter a solution of the two-scale problem is then reconstructed ( downscaling). These results are at variance with the outcome of so-called analogical models, that assume a mean-field-type hypothesis. Finally, we represent the system (∗) as a minimum problem, and interpret the above results in terms of two- and single-scale Γ-convergence.

OS1409 粘弾性複合材料における振動減衰のための内部摩擦の評価(弾性数理解析を用いた材料特性の理解への取り組み(1),オーガナイズドセッション)

機能性を有する制振材料の開発のためには,複合化した粘弾性材料に関する特性評価法の確立が必要であり,新たな制振設計の最適化が可能になる.本研究では,複合材料の微視構造と樹脂の粘弾性特性を考慮して,振動減衰のための内部摩擦に着目した.解析には,微視構造の周期性とラプラス変換した変位に対して漸近展開を適用する.内部摩擦の特性は,ラプラス逆変換した解に調和変動のひずみ入力に対する応力の応答を数値的に求めることにより評価した.樹脂の粘弾性特性は,一般化Maxwellモデルを用いて,複合材料の周波数依存性のある特性に関する評価法を示した.

Thermal-stress concentration near inclusions in viscoelastic random composites

The determination of thermal-stress concentrations near inclusions in viscoelastic random composites is concerned with the prediction of the overall response of random nonlinear viscoelastic multi-component media. The continuum considered here is assumed to be subjected to a finite deformation. First Piola’s stress tensor and deformation gradient are used as conjugate field variables in a fixed reference state. A nonlinear problem is investigated in a second-order approximation theory when the gradient deformation terms higher than second order are neglected. A convex potential function in a thermo-elastic problem and time functionals in a viscoelastic one are used to construct overall constitutive relations. The technique of surface operators developed by R. Hill and others is used to determine stress concentrations near inclusions for nonlinear matrix creep.

A Theory of Thermoviscoelastic Composites Modelled as Interacting Cosserat Continua

In this article we derive a continuum theory for a viscoelastic composite which is modelled as a mixture of a micropolar elastic solid and a micropolar Kelvin-Voigt material. The local forms of balance laws are presented in lagrangian description. Linear constitutive equations are presented for a heat conducting mixture. In contrast with the theories of solid-fluid mixtures, in the present theory the diffusive force depends on relative displacement, relative velocity, relative microrotation and relative microrotation rate.A uniqueness result is established in the context of the linear theory. Finally, the effects of a concentrated heat source are investigated.

Comparison between the relaxation spectra obtained from homogenization models and finite elements simulation for the same composite

The objective of this work is to determine the relaxation spectrum of spherical particles reinforced viscoelastic and isotropic composites from 3D Finite Elements (FE) simulations of the microstructure. The matrix and the reinforcements are assumed to be incompressible and Maxwellian. The spectra obtained from the FE simulations are compared with those obtained from analytical homogenization models. This paper presents the procedure used for generating the FE models as well as the procedure used for obtaining relaxation spectra meeting the thermodynamics requirements imposed on linear viscoelastic materials. It seems that the relaxation spectrum for the microstructure studied in this paper is composed of a negligible continuous part and a discrete part of higher intensity. In any case, the resulting material does not have a Maxwellian behavior.

On the propagation of Lamb Waves in Viscoelastic Composites for SHM Applications

This paper presents a theoretical model for anisotropic wave attenuation in composites. The model has been implemented in a software called FIBREWAVE in order to predict dispersion and attenuation of A0 Lamb wave modes. The required input data are the complex stiffness matrix coefficients of the unidirectional plies of the composites, which have been measured by an immersion technique. Good agreement has been observed between predicted and experimental group velocities and wave attenuations.

Prediction of long-term mechanical behaviour of fibre composites from the observation of micro-buckling appearing during creep compression tests

The axial compressive strength and failure time of IM7/977-2 quasi-isotropic viscoelastoplastic laminates are investigated. Effects of non-linear shear behaviour and fibre misalignment are emphasized because they are important strength-limiting factor in those strongly anisotropic composites which fail by local buckling in the shear mode of deformation. We first describe the basic model of Budiansky [Budiansky B, Fleck NA. Compressive failure of fibre composites. J Mech Phys Solids 1991; 41(1): 183–211], the model of Schapery [Schapery RA. Compressive strength and failure time based on local buckling in viscoelastic composites. Appl Mech Rev 1993; 46(2): S221–8] neglecting non-linear effects in the quasi-elastic solution and finally we adapt the model of Slaughter and Fleck [Slaughter WS, Fleck NA. Viscoelastic micro-buckling of fibre composites. J Appl Mech 1993; 60: 802–6] to predict creep compressive strength for any multi angle laminate. The analysis is formulated in terms of general non-linear viscoelastic viscoplastic behaviour within the kink band. Failure is due to the attainment of a critical failure strain or a critical angle ϕ r in the kink band.

Introduction of damage evolution in a scale transition approach for highly-filled particulate composites

The present paper deals with a non-conventional scale transition for modelling the behaviour of highly-filled particulate composites, starting from a methodology initially proposed by Christoffersen [Christoffersen J. Bonded granulates. J Mech Phys Solids 1983;31:55–83] and recently extended by Nadot et al. [Nadot C, Dragon A, Trumel H, Fanget A. Damage modelling framework for viscoelastic particulate composites via a scale transition approach. J Theor Appl Mech 2006;44(3):553–83] in presence of damage. The model thus obtained is here completed with several ingredients allowing to describe damage evolution and in particular a defect nucleation criterion as well as a closure criterion. These criteria are formulated in terms of displacement, and so as to ensure continuity in terms of macroscopic stress. They are finally introduced in an iterative numerical solving procedure which allows to follow damage evolution as a discrete sequence of interfacial debonding including also eventual closure of defects.

Sound Performance of Multilayered Composites

The purpose of this paper is to study the sound-absorption properties of the multilayered viscoelastic composites with different interface shapes. The results show that in the low frequency, the sound-absorption coefficients of the composites with nonplanar interface are higher than those of the composite with planar interface.

A finite element based investigation on obtaining high material damping over a large frequency range in viscoelastic composites

Various vibration and noise suppression applications require a high loss factor ( tan δ ) over a wide frequency range. Homopolymers often do not meet this requirement. However, the damping properties of polymeric composites can be modulated to achieve this goal. In this paper, we devise a simple finite element based unit cell model to calculate the effective tan δ of a composite as a function of frequency. Using this method, we show that if the relaxation times of the constituents are properly chosen, a flat tan δ response over a wide frequency range can be obtained. Inclusions with multiple layers are seen to be particularly suitable towards this end.