Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and ex... more Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.
ABSTRACT This paper addresses two important phenomena associated with interpretation of experimen... more ABSTRACT This paper addresses two important phenomena associated with interpretation of experimental viscoelastic material property data and is of direct application to composites. (1) The influences of distinct ramp loading functions and of the rise time to full load on experimental material characterizations are investigated analytically and through numerical simulations and their important contributions to accurate material characterization are evaluated. (2) It is further demonstrated that the determination of relaxation and/or creep functions from the same experimental data in real time is a preferable protocol as it avoids additional unnecessary errors introduced through numerical transform inversions. Such numerical and other analytical approximations are evaluated in light of exact material property determinations. Keywords : constitutive viscoelastic relations, material property characterizations (exact & approximate), relaxation/creep function interrelations, simulations of experimen...
Analytical and numerical formulations and simulations are carried out in order to conduct sensiti... more Analytical and numerical formulations and simulations are carried out in order to conduct sensitivity stud- ies of physical parameters motion and amplitude control by viscoelastic piezoelectric and material damping of viscoelastic plates. Numerical simulations in terms of critical parameters, such as relaxation fanetions of the structure and piezoelectric devices, are carried out to evaluate system responses, sensing and structural control.
... computational difficulties, but requires extensive CPU time since it has to be reevaluated fo... more ... computational difficulties, but requires extensive CPU time since it has to be reevaluated for each time step during the Runge-Kutta process, unless some approximate (discrete) scheme is ... Solutions to the above general relation are not obtainable in either analytical or numer ...
ABSTRACT In this study, both an elastic and a viscoelastic constitutive relations are considered ... more ABSTRACT In this study, both an elastic and a viscoelastic constitutive relations are considered for the matrix. Time dependent strains and stresses of the fiber, interphase and matrix are computed and the interaction between the fiber and matrix is examined. Effective Young's moduli for composites are evaluated. Effects of the viscoelastic interfacial layer on the average transverse Young's modulus are also investigated. The numerical evaluation shows that the effective transverse Young's modulus of fiber-reinforced composites are significantly affected by the fiber volume fraction ratio and viscoelastic behavior of the matrix.
An analysis and computational simulations are carried out for the creep divergence and stochastic... more An analysis and computational simulations are carried out for the creep divergence and stochastic delamination failures of lifting surfaces. Divergence times and probabilities of failure are determined for distinct temperature conditions and evaluated. Design criteria based on divergence times and/or times to reach preassigned levels of failure probabilities are examined.
Asphalt concrete pavements exhibit severely graded properties through their thickness due to oxid... more Asphalt concrete pavements exhibit severely graded properties through their thickness due to oxidative aging effects, which are most pronounced at the surface of the pavement and decrease rapidly with depth from the surface. Most of the literature to date has focused on use of layered-elastic models for the consideration of age stiffening. In the current work, a graded viscoelastic model has been implemented within a numerical framework for the simulation of asphalt pavement responses under thermal and mechanical loading. The graded viscoelastic work is extension of the previous work by Paulino and Jin [1], Mukherjee and Paulino [2], and Buttlar et al. [3]. A functionally graded generalized Maxwell model has been used in the development of a constitutive model for asphalt concrete considering aging and temperature gradients. The aging gradient data from laboratory test results reported by Apeagyei [4] is used for obtaining material properties for the graded viscoelastic model. Finite element implementation of the constitutive model incorporates the generalized iso-parametric formulation (GIF) proposed by Kim and Paulino [5], which leads to the graded viscoelastic elements used in this work.
The objective of this work is to present the numerical implementation for the alternative determi... more The objective of this work is to present the numerical implementation for the alternative determination of vis-coelastic material properties without using Poisson's ratios as presented in [1]-[3]. The presented method is based on the 3-D generalized constitutive relations viscoelastic materials with hereditary integrals. The numerical procedures are based on experiments using photogrammetric and tensile testing instrumentation, which provide stress data
The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic E... more The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic Euler-Bernoulli beams subjected to simultaneous bending and twisting. It is shown that the corresponding Timoshenko viscoelastic functions now depend not only on material properties and geometry as they do in elasticity, but also additionally on stresses and their time histories. Possible viscoelastic definitions are formulated and evaluated. In general, the viscoelastic relations are sufficiently complicated so that the elastic-viscoelastic correspondence principle (analogy) cannot be applied. This is particularly true for, but not limited to, elastic shear coefficients which are Poisson ratio dependent. Expressions for equivalent viscoelastic Timoshenko shear functions must, therefore, be derived de novo on a case by case basis, taking in to account specific relaxation moduli, stresses, temperatures and their time histories. Thus the elastic simplicity and generality is lost and hence rendering the use of viscoelastic Timoshenko shear functions as highly impractical. Consequently, it is necessary to directly solve the coupled viscoelastic beam governing relations for bending and twisting deflections by using appropriate solution protocols as discussed herein.
Flutter Initiation Under Steady - State and Accelerated Free Stream Velocities. Harry H. Hilton. ... more Flutter Initiation Under Steady - State and Accelerated Free Stream Velocities. Harry H. Hilton. Craig G. Merrett. Abstract. ... This legacy definition is demonstrable using a Duncan-Ellis flutter engine that replicates the motions of a pitch-plunge wing. ...
Analytical studies are presented which extend the elastic-viscoelastic analogies to stochastic pr... more Analytical studies are presented which extend the elastic-viscoelastic analogies to stochastic processes caused by random linear viscoelastic material properties. Separation of variable as well as integral transform correspondence principles are formulated and discussed in detail. The statistical differential equation of the moment characteristic functional is derived, but rather than solving the highly complex functional equation, solutions are formulated in terms of first and second order statistical properties. Both Gaussian and beta distributions are considered for the probability density distributions of creep and relaxation functions and their effectiveness is evaluated. In order to illustrate the developed general theory, specific examples of beam bending and pressurized hollow cylinders are solved. The influence of various parameters contributing to the creep and relaxation correlation f/mctions is evaluated and the relationship between deterministic and stochastic bounds is also investigated. It is shown that deterministic bounds based on material data spread are unrealistic in the presence of random viscoelastic properties, since the do not correctly predict the limits of this stochastic process.
Piezoelectric efiects are of increasing importance in the control and sensing of structural eleme... more Piezoelectric efiects are of increasing importance in the control and sensing of structural element de∞ections. Elastic piezoelectric theory has been extensively developed (Leibowitz & Vinson 1993). Hilton et al. (1997) have presented an extended bibliography and dis- cussed past contributions as well as formulated an analytical nonlinear theory of anisotropic piezoelectric-thermo-viscoelasticity. Only a limited number of analytical and experimental publications on linear piezo-viscoelastic materials may be found in the literature (Holloway & Vinogradov 1997, Vinogradov & Holloway 1997). Yi et al. (1996) have formulated flnite element solutions to demonstrate viscoelastic material damping. Hilton et al. (1997, 1998a, b) and Beldica et al. (1998a, b, c) have applied this theory to a number of linear viscoelastic bending and aero-viscoelastic problems, such as creep ∞utter and torsional divergence and the response of piezo-viscoelastic structures to aerodynamic noise. Yi et al. (1997)...
Temperature and moisture content effects on viscoelastic responses of GY70/339, T300/934 and kevl... more Temperature and moisture content effects on viscoelastic responses of GY70/339, T300/934 and kevlar-epoxy laminated composites are investigated using finite element analyses. Time-dependent strains and stresses for these composite plates subjected to moisture absorption and desorption cycles are presented. The results show kevlar-epoxy laminates to be more strongly affected by hygrothermal loads than those made of graphite fibers.
Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and ex... more Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.
ABSTRACT This paper addresses two important phenomena associated with interpretation of experimen... more ABSTRACT This paper addresses two important phenomena associated with interpretation of experimental viscoelastic material property data and is of direct application to composites. (1) The influences of distinct ramp loading functions and of the rise time to full load on experimental material characterizations are investigated analytically and through numerical simulations and their important contributions to accurate material characterization are evaluated. (2) It is further demonstrated that the determination of relaxation and/or creep functions from the same experimental data in real time is a preferable protocol as it avoids additional unnecessary errors introduced through numerical transform inversions. Such numerical and other analytical approximations are evaluated in light of exact material property determinations. Keywords : constitutive viscoelastic relations, material property characterizations (exact & approximate), relaxation/creep function interrelations, simulations of experimen...
Analytical and numerical formulations and simulations are carried out in order to conduct sensiti... more Analytical and numerical formulations and simulations are carried out in order to conduct sensitivity stud- ies of physical parameters motion and amplitude control by viscoelastic piezoelectric and material damping of viscoelastic plates. Numerical simulations in terms of critical parameters, such as relaxation fanetions of the structure and piezoelectric devices, are carried out to evaluate system responses, sensing and structural control.
... computational difficulties, but requires extensive CPU time since it has to be reevaluated fo... more ... computational difficulties, but requires extensive CPU time since it has to be reevaluated for each time step during the Runge-Kutta process, unless some approximate (discrete) scheme is ... Solutions to the above general relation are not obtainable in either analytical or numer ...
ABSTRACT In this study, both an elastic and a viscoelastic constitutive relations are considered ... more ABSTRACT In this study, both an elastic and a viscoelastic constitutive relations are considered for the matrix. Time dependent strains and stresses of the fiber, interphase and matrix are computed and the interaction between the fiber and matrix is examined. Effective Young's moduli for composites are evaluated. Effects of the viscoelastic interfacial layer on the average transverse Young's modulus are also investigated. The numerical evaluation shows that the effective transverse Young's modulus of fiber-reinforced composites are significantly affected by the fiber volume fraction ratio and viscoelastic behavior of the matrix.
An analysis and computational simulations are carried out for the creep divergence and stochastic... more An analysis and computational simulations are carried out for the creep divergence and stochastic delamination failures of lifting surfaces. Divergence times and probabilities of failure are determined for distinct temperature conditions and evaluated. Design criteria based on divergence times and/or times to reach preassigned levels of failure probabilities are examined.
Asphalt concrete pavements exhibit severely graded properties through their thickness due to oxid... more Asphalt concrete pavements exhibit severely graded properties through their thickness due to oxidative aging effects, which are most pronounced at the surface of the pavement and decrease rapidly with depth from the surface. Most of the literature to date has focused on use of layered-elastic models for the consideration of age stiffening. In the current work, a graded viscoelastic model has been implemented within a numerical framework for the simulation of asphalt pavement responses under thermal and mechanical loading. The graded viscoelastic work is extension of the previous work by Paulino and Jin [1], Mukherjee and Paulino [2], and Buttlar et al. [3]. A functionally graded generalized Maxwell model has been used in the development of a constitutive model for asphalt concrete considering aging and temperature gradients. The aging gradient data from laboratory test results reported by Apeagyei [4] is used for obtaining material properties for the graded viscoelastic model. Finite element implementation of the constitutive model incorporates the generalized iso-parametric formulation (GIF) proposed by Kim and Paulino [5], which leads to the graded viscoelastic elements used in this work.
The objective of this work is to present the numerical implementation for the alternative determi... more The objective of this work is to present the numerical implementation for the alternative determination of vis-coelastic material properties without using Poisson's ratios as presented in [1]-[3]. The presented method is based on the 3-D generalized constitutive relations viscoelastic materials with hereditary integrals. The numerical procedures are based on experiments using photogrammetric and tensile testing instrumentation, which provide stress data
The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic E... more The concept of elastic Timoshenko shear coefficients is used as a guide for linear viscoelastic Euler-Bernoulli beams subjected to simultaneous bending and twisting. It is shown that the corresponding Timoshenko viscoelastic functions now depend not only on material properties and geometry as they do in elasticity, but also additionally on stresses and their time histories. Possible viscoelastic definitions are formulated and evaluated. In general, the viscoelastic relations are sufficiently complicated so that the elastic-viscoelastic correspondence principle (analogy) cannot be applied. This is particularly true for, but not limited to, elastic shear coefficients which are Poisson ratio dependent. Expressions for equivalent viscoelastic Timoshenko shear functions must, therefore, be derived de novo on a case by case basis, taking in to account specific relaxation moduli, stresses, temperatures and their time histories. Thus the elastic simplicity and generality is lost and hence rendering the use of viscoelastic Timoshenko shear functions as highly impractical. Consequently, it is necessary to directly solve the coupled viscoelastic beam governing relations for bending and twisting deflections by using appropriate solution protocols as discussed herein.
Flutter Initiation Under Steady - State and Accelerated Free Stream Velocities. Harry H. Hilton. ... more Flutter Initiation Under Steady - State and Accelerated Free Stream Velocities. Harry H. Hilton. Craig G. Merrett. Abstract. ... This legacy definition is demonstrable using a Duncan-Ellis flutter engine that replicates the motions of a pitch-plunge wing. ...
Analytical studies are presented which extend the elastic-viscoelastic analogies to stochastic pr... more Analytical studies are presented which extend the elastic-viscoelastic analogies to stochastic processes caused by random linear viscoelastic material properties. Separation of variable as well as integral transform correspondence principles are formulated and discussed in detail. The statistical differential equation of the moment characteristic functional is derived, but rather than solving the highly complex functional equation, solutions are formulated in terms of first and second order statistical properties. Both Gaussian and beta distributions are considered for the probability density distributions of creep and relaxation functions and their effectiveness is evaluated. In order to illustrate the developed general theory, specific examples of beam bending and pressurized hollow cylinders are solved. The influence of various parameters contributing to the creep and relaxation correlation f/mctions is evaluated and the relationship between deterministic and stochastic bounds is also investigated. It is shown that deterministic bounds based on material data spread are unrealistic in the presence of random viscoelastic properties, since the do not correctly predict the limits of this stochastic process.
Piezoelectric efiects are of increasing importance in the control and sensing of structural eleme... more Piezoelectric efiects are of increasing importance in the control and sensing of structural element de∞ections. Elastic piezoelectric theory has been extensively developed (Leibowitz & Vinson 1993). Hilton et al. (1997) have presented an extended bibliography and dis- cussed past contributions as well as formulated an analytical nonlinear theory of anisotropic piezoelectric-thermo-viscoelasticity. Only a limited number of analytical and experimental publications on linear piezo-viscoelastic materials may be found in the literature (Holloway & Vinogradov 1997, Vinogradov & Holloway 1997). Yi et al. (1996) have formulated flnite element solutions to demonstrate viscoelastic material damping. Hilton et al. (1997, 1998a, b) and Beldica et al. (1998a, b, c) have applied this theory to a number of linear viscoelastic bending and aero-viscoelastic problems, such as creep ∞utter and torsional divergence and the response of piezo-viscoelastic structures to aerodynamic noise. Yi et al. (1997)...
Temperature and moisture content effects on viscoelastic responses of GY70/339, T300/934 and kevl... more Temperature and moisture content effects on viscoelastic responses of GY70/339, T300/934 and kevlar-epoxy laminated composites are investigated using finite element analyses. Time-dependent strains and stresses for these composite plates subjected to moisture absorption and desorption cycles are presented. The results show kevlar-epoxy laminates to be more strongly affected by hygrothermal loads than those made of graphite fibers.
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Papers by Harry Hilton