Elastic-viscoelastic Correspondence Principle Research Articles

Axisymmetric viscoelastic response of flexible pipes in time domain

The challenges for determining the mechanical behavior of flexible pipes mainly arise from highly non-linear geometrical and material properties and complex contact interaction conditions between and within layers components. This paper develops an innovative model to investigate the linear viscoelastic behavior of flexible pipes under axisymmetric loads in time domain. The model is derived from an equivalent linear elastic axisymmetric model by invoking the elastic-viscoelastic correspondence principle. Analytical formulations that describe the behavior of the metallic helical layers based on a combination of differential geometry concepts and Clebsch–Kirchhoff equilibrium equations for initially curved slender elastic rods are presented. The elastic response of the homogenous polymeric cylindrical layers is also presented. The assemblage of both types of governing algebraic equations that approximate analytical solutions for force and moment distributions, deformations in each layer, as well as contact pressure between near layers, taking time-dependent characteristics of polymeric layers into account are provided and it is clear that the relationship between axial force and elongation is non-linear and encompasses a hysteretic response. Besides, the creep behavior in axial direction can also be found. Some insights into the differences in the behavior for several loading conditions are discussed by considering variable frequencies.

Viscoelastic Response Modelling of a Pavement under Moving Load

This paper demonstrates the application of a generalized layered linear viscoelastic (LVE) analysis for estimating flexible pavements’ structural response. The procedure is based on the Multi-Layered Elastic Theory (MLET) and the elastic-viscoelastic correspondence principle using a numerical inverse Laplace transform. A comparison of the direct layered viscoelastic responses with approximate solutions based on the elastic collocation method was also carried out. Furthermore, it is proposed to use the collocation method using LVE solutions at selected time durations in order to improve the accuracy of the elastic collocation method. The LVE collocation method was further extended for analysis of moving loads. The method was illustrated by analysing a pavement structure subjected to moving wheel loads of 30, 50, 60 and 80 kN using a Heavy Vehicle Simulator (HVS). The various responses (stresses and strains) in the pavement, at different pavement temperatures, were measured using various types of sensors installed in the structure. The LVE calculations agreed very well with the measurements.

Monotonic and fatigue performance of RC beams strengthened with a polyurea coating system

This paper has been conducted to evaluate fatigue and monotonic behavior of concrete beams strengthened with a polyurea coating system. Ease of application and multi-hazard benefits of polyurea has made it useful in retrofit–repair situations. Rather than blast or impact mitigation, polyurea has the capability of flexural and shear reinforcement for structural members. In this research, parametric study has been done to describe the flexural capacity of coated beams. Moreover, theoretical model was developed to predict the maximum deflection of strengthened beams under cyclic service loads. In order to validate the models, large size reinforced concrete beams were fabricated and externally strengthened in two levels of polyurea thickness. Beams were tested under four-point monotonic and fatigue loading. The relationship between deflection, coating thickness and number of cycles was studied and analyzed. In addition, the elastic–viscoelastic correspondence principle was used to evaluate the damage mechanism of the coating system in repetitive load condition. Results indicated that application of polyurea, improves the flexural capacity as well as ductility of RC beams, additionally, the correspondence principle represented an acceptable model for damage growth and fracture healing of the external polyurea coating under complex cyclic loading.

Creep and relaxation contribution tensors for spheroidal pores in hereditary solids: fraction-exponential operators approach

In this paper, we introduce creep and relaxation contribution tensors that describe the effect of individual pores on the overall viscoelastic properties of a porous material. Explicit analytical expressions for these tensors are obtained using the elastic–viscoelastic correspondence principle and the Laplace transform. This becomes possible when viscoelastic properties are expressed in terms of fraction-exponential operators of Rabotnov (J Appl Math Mech (PMM) 12:53–62, 1948). Creep and relaxation contribution tensors can serve as the basic building blocks for the calculation of overall viscoelastic properties of porous hereditary materials.

Interface effects on the creep characteristics of asphalt concrete

A micromechanical creep model is presented to predict the creep behavior of asphalt concrete (AC) and investigate the effect of imperfect interface between asphalt mastic and aggregates on the viscoelastic properties of AC. The linear spring layer model is introduced to characterize the interface imperfection. Based on the modified Mori–Tanaka method, the micromechanical model is developed. To describe the viscoelastic properties of AC with imperfect interface, micromechanical creep compliance formulation is obtained by incorporating the elastic–viscoelastic correspondence principle. The present prediction is compared with available experimental data in the literature to verify the proposed method. It is found that the micromechanical creep model has the capability to predict the creep behavior of AC. Interface effects on the creep behavior of AC are explored using the developed model. It is concluded that the imperfect interface between asphalt mastic and aggregates has a significant influence on the overall mechanical behavior of AC, and that the interfacial damage should be controlled within a certain extent.

Homogenization theory for designing graded viscoelastic sonic crystals**Project supported by the National Basic Research Program of China (Grant No. 2011CB610301).

In this paper, we propose a homogenization theory for designing graded viscoelastic sonic crystals (VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material. We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC. The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement. According to the relation of the effective loss factor to the filling fraction, a graded VSC plate is easily and quickly designed. Then, the graded VSC may have potential applications in the vibration absorption and noise reduction fields.

Uniaxial Compression Creep Prediction of Asphalt Mixture Using the Eshelby Equivalent Inclusion Method

Asphalt mixture was simply treated as a two-phase composite, in which coarse aggregates are embedded into asphalt mastic matrix. According to the elastic-viscoelastic correspondence principle, an elastic micromechanical method is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded into viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different stress conditions in order to determine the matrix constitutive parameters, the presented framework is validated by comparison with the experiment, and then some predictions to uniaxial compression creep behavior of asphalt mixture in different stress conditions are given.

Dynamic response of a frame-foundation-soil system: a coupled BEM–FEM procedure and a GPU implementation

Graphics processing units have experienced an increasing demand for general-purpose computer applications such as engineering, science, finance, among other areas. This study uses such devices to analyze the performance of a code designed to evaluate the dynamic response of frame-foundation-soil system. In the present article, a direct version of the boundary element method (BEM) is applied to synthesize the 3D dynamic compliance matrix of a rigid and massless foundation interacting with unbounded soil profiles. The foundation compliance matrix is coupled to a frame, modeled by the finite element method (FEM) leading to the dynamic response of a coupled frame-foundation-soil system. The direct version of the 3D boundary element method is built based on the stationary fundamental solution of an elastic full-space. Viscoelastic effects are incorporated by means of the elastic–viscoelastic correspondence principle. The article describes the methodology applied to couple rigid bodies with the BEM mesh. The soil-foundation interaction result is given in terms of a dynamic compliance matrix for a rigid and massless foundation. The frame structural analysis is based on FEM where bar and beam elements are coupled. This strategy allows performing frequency domain analysis of such structural systems. The performance analysis is done by comparing two codes: one was exclusively developed in C language and the other one in CUDA C (Compute Unified Device Architecture). The level of speedup was achieved by implementing some functions in the frame model, i.e., on the FEM based code.

Bulk and shear characterization of bituminous mixtures in the linear viscoelastic domain

Traffic loads and temperature variations produce three-dimensional stress–strain fields inside road pavements, and therefore the characterization of bituminous mixtures in different deformation modes is important for prediction of the performance of pavement structures. This paper presents a methodology for the bulk and shear characterization of bituminous mixtures in the linear viscoelastic domain, under the hypothesis of material isotropy, by means of uniaxial harmonic tests with the measurement of axial and transverse strains. The theoretical approach was based on the application of the elastic–viscoelastic correspondence principle and was validated by performing tension–compression tests at selected frequencies and temperatures on asphalt concrete specimens characterized by different volumetric properties. The results showed that since uniaxial tests induced both volume and shape variations, the simultaneous measurement of the complex bulk and shear moduli was possible. The validity of the time–temperature superposition principle was also verified for both deformation modes, allowing the construction of master curves for the bulk and shear moduli. The results also showed that the total dissipated energy could be decomposed into its volumetric and deviatoric fractions with excellent accuracy.

A Micromechanical framework with aggregate-mastic interface effect for predicting uniaxial compression creep of asphalt mixture

According to the elastic-viscoelastic correspondence principle, an elastic micromechanical framework taking the inclusion-matrix interface effect into account is extended for predicting viscoelastic properties of asphalt mixture, which is simply treated as elastic coarse aggregate inclusions periodically and isotropically embedded in a viscoelastic asphalt mastic matrix. The Burgers model is adopted for characterizing the matrix mechanical behavior, so that the homogenized relaxation modulus of asphalt mixture in compression creep is derived. After a series of uniaxial compression creep tests are performed on asphalt mastic in different temperature and stress conditions in order to determine the matrix constitutive parameters, the framework presented is validated by comparison with the experiment, and then some predictions of uniaxial compression creep behavior of asphalt mixture in different temperature and stress conditions are given.

Testing and analysis of viscoelastic characteristics of solidifying concrete pavement slabs

To accurately estimate the tensile stress distribution in concrete pavement slabs, their viscoelastic characteristics must be clearly identified, because in a drying concrete slab, creep and stress relaxation occur in a complex manner over a long time. In this study, a restrained ring test was conducted to determine the viscoelastic characteristics of a concrete pavement slab. Finite Element Analysis (FEA) was performed to simulate the restrained ring test using the solidifying viscoelastic properties obtained from the modified elastic-viscoelastic correspondence principle to verify the effect of the viscoelastic material properties. The tensile stress calculated by the viscoelastic analysis was observed to be ∼50% of that obtained from the elastic analysis. The FEA was performed under assumed environmental conditions for the elastic and viscoelastic models of a concrete pavement. Further, the maximum tensile stress based on the viscoelastic model was observed to be 45–55% less than that based on the elastic model owing to stress relaxation. It is concluded that the model that considers the solidifying viscoelastic properties shows better analysis results for tensile stress distribution in a concrete pavement. With better and more accurate estimates of the concrete pavement responses, a pavement that is more structurally sound can be designed.

G0310202 押込み試験による予ひずみを考慮したガスケットの長期・高温粘弾性特性評価(材料力学部門一般セッション:変形・ひずみ(2))

Gasket stresses in flanged joints decrease due to creep deformation of gaskets. Prediction of long-term viscoelastic properties of a gasket is important to ensure the tightness of flange joint for a long-term use, especially in elevated temperature applications. Nanoindentation creep test was carried out using TMA with Berkovich indenter to evaluate the viscoelastic characteristics of a PTFE based sheet gasket. The time-temperature superposition principle using W.L.F equation was applied to obtain the master curve of the creep compliance of gasket material at elevated temperature. The elastic-viscoelastic correspondence principle waz also applied to estimate the gasket creep strain in the flanges from the master curve of the creep compliance. It was able to obtain equally prediction equation with results of HPIS Z 105 test by taking into account the pre-strain. In order to obtain a creep strain predictive expression, it is necessary to consider the prestrain. Creep strain predictive expression is useful for estimating the long-term creep modification in a flange with a high temperature.

Micromechanical creep models for asphalt-based multi-phase particle-reinforced composites with viscoelastic imperfect interface

A methodology to account for the interface effect on the viscoelastic behavior of asphalt-based multi-phase particle-reinforced composites is presented. A Kelvin–Voigt type viscoelastic interface is introduced first to simulate the imperfect interface between asphalt mastic and particles. The concept of “effective” particle properties is used to take into account the viscoelastic characteristic of the interface in an averaged manner. Then, the micromechanical creep model is developed based on the Mori–Tanaka method, and further solved analytically by incorporating the elastic–viscoelastic correspondence principle. Tests are conducted on the three types of asphalt concrete with different microstructures, and then compared with the predicted results. The results indicate that the developed micromechanical model has the capability to predict the creep behavior observed from the asphalt concrete. Finally, the effects of particle size, viscoelastic characteristic of asphalt mastic, the different rheological models for simulating asphalt mastic, elastic properties of particles, volume fraction of particles, and particularly interface imperfection on the creep behavior of asphalt concrete are further investigated.

Anisotropic Characterization of Crack Growth in the Tertiary Flow of Asphalt Mixtures in Compression

Asphalt mixtures exhibit primary, secondary, and tertiary stages in sequence during a rutting deterioration. Many field asphalt pavements are still in service even when the asphalt layer is in the tertiary stage, and rehabilitation is not performed until a significant amount of rutting accompanied by numerous macrocracks is observed. The objective of this study was to provide a mechanistic method to model the anisotropic cracking of the asphalt mixtures in compression during the tertiary stage of rutting. Laboratory tests including nondestructive and destructive tests were performed to obtain the viscoelastic and viscofracture properties of the asphalt mixtures. Each of the measured axial and radial total strains in the destructive tests were decomposed into elastic, plastic, viscoelastic, viscoplastic, and viscofracture strains using the pseudostrain method in an extended elastic-viscoelastic correspondence principle. The viscofracture strains are caused by the crack growth, which is primarily signaled by the increase of phase angle in the tertiary flow. The viscofracture properties are characterized using the anisotropic damage densities (i.e., the ratio of the lost area caused by cracks to the original total area in orthogonal directions). Using the decomposed axial and radial viscofracture strains, the axial and radial damage densities were determined by using a dissipated pseudostrain energy balance principle and a geometric analysis of the cracks, respectively. Anisotropic pseudo J-integral Paris' laws in terms of damage densities were used to characterize the evolution of the cracks in compression. The material constants in the Paris' law are determined and found to be highly correlated. These tests, analysis, and modeling were performed on different asphalt mixtures with two binders, two air void contents, and three aging periods. Consistent results were obtained; for instance, a stiffer asphalt mixture is demonstrated to have a higher modulus, a lower phase angle, a greater flow number, and a larger n1 value (exponent of Paris' law). The calculation of the orientation of cracks demonstrates that the asphalt mixture with 4% air voids has a brittle fracture and a splitting crack mode, whereas the asphalt mixture with 7% air voids tends to have a ductile fracture and a diagonal sliding crack mode. Cracks of the asphalt mixtures in compression are inclined to propagate along the direction of the external compressive load.

Piezoelectric Effect on the Buckling of Piezoelectric Thin Film with Viscoelastic Substrate

AbstractThis work aims to study the buckling kinetic process of a piezoelectric thin film (nanoribbon) bonded to a viscoelastic compliant layer with rigid support. The piezoelectric thin film is assumed to be poled in the thickness direction and is governed by the nonlinear coupled electromechanical equations. Subsequently, on the basis of the classical elastic-viscoelastic correspondence principle, the kinetic process of the thin film buckling under the intermediate stress state is analyzed in a systematic manner. In particular the piezoelectric effect is examined with respect to the critical wavelength, the wavelength of the fastest growing mode, the critical stress, and the fastest growth rate in detail. The results evince that the piezoelectricity has an evident stiffening effect on the kinetic buckling process of the thin film with viscoelastic substrate.

Stability of viscoelastic continuum with negative‐stiffness inclusions in the low‐frequency range

The stability of viscoelastic composites with negative stiffness (NS) inclusions and their associated extreme mechanical properties are studied with time‐domain finite element analysis and composite theory. In the finite element analysis, the stability of the plane‐strain, two‐phase NS composite is evaluated by monitoring the stress divergence under uniaxial straining. In addition, 2D and 3D two‐phase NS composites are studied by using composite theories and the elastic–viscoelastic correspondence principle. Effective stiffness and damping anomalies are observed, and the stability of the composites is evaluated. In the low frequency regime, stability conditions for purely elastic systems are suitable to estimate the stability of the viscoelastic composites. This is verified with the finite element analysis. For the 2D problem, the finite element analysis and composite theory agree well with each other in terms of the overall properties and stability. For the 3D problem, only the results obtained from the composite theory are presented. Our analysis shows that the extreme mechanical properties for both of the 2D and 3D cases are located near the strong ellipticity boundary. When the matrix modulus is suitably chosen to satisfy all stability conditions, the effective stiffness softening anomaly (i.e., damping enhancement) may be in the stability range. The effective stiffness enhancement locates in the non‐elliptic range of the negative inclusion bulk modulus parameter space.

Investigation of the thickness variability and material heterogeneity effects on free vibration of the viscoelastic circular plates

The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions. It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously. The complex modulus approach is employed in conjunction with the elastic–viscoelastic correspondence principle to obtain the solution. The governing equations are solved by means of a power series solution. Finally, a sensitivity analysis including evaluation of effects of various edge conditions, thickness variations, coefficients of the elastic foundation, and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.

An Analytical Model to Evaluate the Static Soil Pressure Throughout Geological Era

In this study, the time dependent characteristics of the soil pressure coefficient is theoretically investigated and a new model is developed to evaluate the static soil pressure in a normally consolidated soil deposit during geological era. The volumetric deformation of soil is described by the Kelvin model, while its shear deformation is represented by the modified Maxwell model assuming the shear- creep relationship as a linear function of the time logarithm. By employing the “elastic-viscoelastic correspondence principle”, the coefficient of soil pressure is found as a function of time, indicating an increase within the geological time span

A micromechanics-based viscoelastic model for nanocomposites with imperfect interface

A viscoelastic interface model is proposed to study the effective mechanical responses of nanocomposites filled with carbon nanotubes. It is incorporated with the Mori–Tanaka method and the elastic-viscoelastic correspondence principle. The effective dynamic stiffness and damping of randomly oriented nanocomposites are investigated with the consideration of imperfect interfacial condition between the filler and matrix as well as the concentration and aspect ratio of fillers. Comparisons are performed between the model-based simulation and the experimental data for a specific type of multi-walled carbon nanotube reinforced elastomer nanocomposites to demonstrate the potential of the proposed framework.

A power series solution for vibration and complex modal stress analyses of variable thickness viscoelastic two-directional FGM circular plates on elastic foundations

In the present paper, a power series solution is developed for free vibration and damping analyses of viscoelastic functionally graded plates with variable thickness on elastic foundations. It is assumed that the material properties of the functionally graded material (FGM) vary in the transverse and radial directions, simultaneously. Therefore, the presented solution can be employed for the transversely-graded and radially-graded viscoelastic circular plates, as special cases. In addition to the edge conditions, the plate may be resting on a two-parameter elastic foundation. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A sensitivity analysis including effects of various edge conditions, geometric parameters, coefficients of the elastic foundation, parameters of the functionally graded material, and material loss factor is carried out. In the present paper, concept of the complex modal stresses of the viscoelastic plates is discussed in detail.