Numerical finite element formulation of the Schapery non-linear viscoelastic material model

doi:10.1002/NME.861

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Numerical finite element formulation of the Schapery non-linear viscoelastic material model

Journal Article•DOI•

Numerical finite element formulation of the Schapery non-linear viscoelastic material model

Rami Haj-Ali¹, Anastasia Muliana¹•Institutions (1)

07 Jan 2004-International Journal for Numerical Methods in Engineering (John Wiley & Sons, Ltd.)-Vol. 59, Iss: 1, pp 25-45

TL;DR: In this paper, a numerical integration method for the non-linear viscoelastic behavior of isotropic materials and structures is presented, where the Schapery's 3D nonlinear material model is integrated within a displacement-based finite element (FE) environment.

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Abstract: This study presents a numerical integration method for the non-linear viscoelastic behaviour of isotropic materials and structures. The Schapery's three-dimensional (3D) non-linear viscoelastic material model is integrated within a displacement-based finite element (FE) environment. The deviatoric and volumetric responses are decoupled and the strain vector is decomposed into instantaneous and hereditary parts. The hereditary strains are updated at the end of each time increment using a recursive formulation. The constitutive equations are expressed in an incremental form for each time step, assuming a constant incremental strain rate. A new iterative procedure with predictor–corrector type steps is combined with the recursive integration method. A general polynomial form for the parameters of the non-linear Schapery model is proposed. The consistent algorithmic tangent stiffness matrix is realized and used to enhance convergence and help achieve a correct convergent state. Verifications of the proposed numerical formulation are performed and compared with a previous work using experimental data for a glassy amorphous polymer PMMA. Copyright © 2003 John Wiley & Sons, Ltd.

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Journal Article•DOI•

A thermo-viscoelastic-viscoplastic-viscodamage constitutive model for asphaltic materials

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Masoud K. Darabi¹, Rashid K. Abu Al-Rub¹, Eyad Masad², Eyad Masad¹, Chien-Wei Huang¹, Dallas N. Little¹ - Show less +2 more•Institutions (2)

Texas A&M University¹, Texas A&M University at Qatar²

01 Jan 2011-International Journal of Solids and Structures

TL;DR: In this paper, a temperature-dependent viscodamage model is proposed and coupled to the temperaturedependent Schapery's nonlinear viscoelasticity and the temperature dependent Perzyna's viscoplasticity constitutive model presented in Abu Al-Rub et al. (2009) in order to model the nonlinear constitutive behavior of asphalt mixes.

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187 citations

Cites background or methods from "Numerical finite element formulatio..."

...(9), the deviatoric strain tensor enve;tij and the volumetric strain e nve;t kk can be expressed in terms of the hereditary integrals, such that (Haj-Ali and Muliana, 2004): enve;tij ¼ 1 2 gt0J0 þ gt1gt2 XN n¼1 Jn gt1gt2 XN n¼1 Jn 1 expð knDwtÞ knDw t " # Stij 1 2 gt1 XN n¼1 Jn expð knDwtÞqt Dtij;n…...
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...…integrals are updated at the end of every converged time increment, which will be used for the next time increment, and are expressed as follows (Haj-Ali and Muliana, 2004): qtij;n ¼ exp knDw t qt Dtij;n þ gt2Stij gt Dt2 St Dtij 1 exp knDwt knDw t ; ð47Þ qtkk;n ¼ exp knDw t qt Dtkk;n þ gt2rtkk…...
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...(9), the deviatoric strain tensor e ij and the volumetric strain e nve;t kk can be expressed in terms of the hereditary integrals, such that (Haj-Ali and Muliana, 2004):...
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...The hereditary integrals are updated at the end of every converged time increment, which will be used for the next time increment, and are expressed as follows (Haj-Ali and Muliana, 2004):...
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...Furthermore, Touati and Cederbaum (1998), Haj-Ali and Muliana (2004), Sadd et al. (2004) and Huang et al. (2007) have developed numerical schemes for implementation of Schapery’s constitutive model in finite element (FE) codes....
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Journal Article•DOI•

A micro-damage healing model that improves prediction of fatigue life in asphalt mixes

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Rashid K. Abu Al-Rub¹, Masoud K. Darabi¹, Dallas N. Little¹, Eyad Masad¹, Eyad Masad² - Show less +1 more•Institutions (2)

Texas A&M University¹, Texas A&M University at Qatar²

01 Nov 2010-International Journal of Engineering Science

TL;DR: A micro-damage healing model that improves the ability of an integrated nonlinear viscoelastic, viscoplastic, and viscodamage constitutive model based on continuum damage mechanics for predicting the fatigue life of asphalt paving mixtures is developed and validated.

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155 citations

Additional excerpts

...The hereditary integrals are updated at the end of every converged time increment, and are used for the subsequent time increment, and are expressed as follows [16]: qij;n 1⁄4 expð knDw Þqt Dt ij;n þ g2Sij g Dt 2 S Dt ij 1 expð knDwÞ knDw t ; ð43Þ qkk;n 1⁄4 expð knDw Þqt Dt kk;n þ g2 rkk g Dt 2 r Dt kk 1 expð knDwÞ knDw t : ð44Þ The increment of the viscoplastic strain in Eqs....
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...Haj-Ali and Muliana [16] developed an iterative–recursive numerical algorithm for finite element implementation of the Schapery’s viscoelastic three-dimensional model....
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Journal Article•DOI•

Prediction of nonlinear viscoelastic behavior of polymeric composites using an artificial neural network

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Marwan Al-Haik¹, M. Y. Hussaini¹, Hamid Garmestani²•Institutions (2)

Florida State University¹, Georgia Institute of Technology²

01 Jul 2006-International Journal of Plasticity

TL;DR: In this paper, a nonlinear viscoelastic constitutive model is developed, and its material parameters are determined by fitting it to creep test data, and an alternative model based on an artificial neural network (ANN) is developed to predict the stress relaxation of the polymer matrix composite.

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111 citations

Cites background from "Numerical finite element formulatio..."

...Several variants of Schapery s approach have been proposed to describe the nonlinear time-dependent response of composites (Papanicolaou et al., 2004; Haj-Ali and Muliana, 2004)....
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Journal Article•DOI•

Nonlinear viscoelastic analysis of unaged and aged asphalt binders

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Eyad Masad¹, Chien-Wei Huang¹, Gordon Airey², Anastasia Muliana¹•Institutions (2)

Texas A&M University¹, University of Nottingham²

01 Nov 2008-Construction and Building Materials

TL;DR: In this paper, the authors present analyses of the nonlinear viscoelastic behavior of unaged and aged asphalt binders tested using a dynamic shear rheometer (DSR) at several temperatures and frequencies.

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104 citations

Journal Article•DOI•

A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part I: Theory

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Rashid K. Abu Al-Rub¹, Masoud K. Darabi¹•Institutions (1)

Texas A&M University¹

01 Jul 2012-International Journal of Plasticity

TL;DR: A general thermodynamic-based framework for deriving coupled temperature-dependent viscoelasticity, viscoplasticity and micro-damage healing constitutive models for constitutive modeling of time and rate-dependent materials is presented in this paper.

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103 citations

Cites background from "Numerical finite element formulatio..."

...Several authors have extended the one-dimensional (1D) Schapery’s constitutive theory to the three-dimensional (3D) viscoelastic models (Henriksen, 1984; Lai and Bakker, 1996; Touati and Cederbaum, 1998; Beijer and Spoormaker, 2002; Haj-Ali and Muliana, 2004; Levesque et al., 2004)....
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References

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Journal Article•DOI•

Thermomechanical analysis of viscoelastic solids

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Robert L. Taylor¹, Karl S. Pister¹, Gerald L. Goudreau¹•Institutions (1)

University of California, Berkeley¹

01 Jan 1970-International Journal for Numerical Methods in Engineering

TL;DR: In this paper, the authors developed a computational algorithm for the solution of the uncoupled, quasi-static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation.

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Abstract: SUMMARY This paper is concerned with the development of a computational algorithm for the solution of the uncoupled, quasi-static boundary value problem for a linear viscoelastic solid undergoing thermal and mechanical deformation. The method evolves from a finite element discretization of a stationary value problem, leading to the solution of a system of linear integral equations determining the motion of the solid. An illustrative example is included.

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381 citations

"Numerical finite element formulatio..." refers methods in this paper

...A recurrence numerical algorithm for linear viscoelastic integral has been proposed by Taylor et al. [15]....
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...The linearized stress update part of this study employs the numerical formulation previously derived by Taylor [15], Henriksen [3], and Lai and Bakker [6]....
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Journal Article•DOI•

3-D schapery representation for non-linear viscoelasticity and finite element implementation

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J. Lai¹, A. Bakker¹•Institutions (1)

Delft University of Technology¹

01 Jul 1996-Computational Mechanics

TL;DR: In this paper, a three-dimensional constitutive model incorporating the effects of temperature and physical ageing is developed for isotropic non-linear viscoelastic materials, with the hereditary integral updated at the end of each time increment by recursive computation.

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Abstract: On the basis of the one-dimensional Schapery representation for non-linear viscoelasticity, a three-dimensional constitutive model incorporating the effects of temperature and physical ageing is developed for isotropic non-linear viscoelastic materials. Adopting the assumption that the hydrostatic and deviatoric responses are uncoupled, the contitutive equation is expressed in incremental form for both compressible and incompressible materials, with the hereditary integral updated at the end of each time increment by recursive computation. The proposed model is implemented in the finite element package MARC. Numerical examples are given to demonstrate the effectiveness of the model and the numerical algorithms.

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181 citations

"Numerical finite element formulatio..." refers background or methods or result in this paper

...Equations (26) and (27) are identical to the linearized relations developed by Lai and Bakker [6]....
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...The current constitutive modelling approach modi es that of Lai and Bakker [6]....
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...The linearized stress update part of this study employs the numerical formulation previously derived by Taylor [15], Henriksen [3], and Lai and Bakker [6]....
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...Calibration and veri cation of the proposed numerical model are performed with test results on glassy amorphous polymer material (PMMA) reported by Lai and Bakker [6]....
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...Henriksen [3], and Lai and Bakker [6] used a similar recursive algorithm for the non-linear constitutive integral....
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Journal Article•DOI•

Nonlinear viscoelastic stress analysis—a finite element approach

[...]

Mogens Henriksen¹•Institutions (1)

Texas A&M University¹

01 Jan 1984-Computers & Structures

TL;DR: In this article, a finite element algorithm was developed for analysis of nonlinear viscoelastic materials, based on Schapery's integral constitutive law, which is used to describe viscoels behavior.

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119 citations

Journal Article•DOI•

A finite element analysis of adhesively bonded composite joints with moisture diffusion and delayed failure

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Samit Roy¹, J. N. Reddy¹•Institutions (1)

Virginia Tech¹

01 Jan 1988-Computers & Structures

TL;DR: In this article, a two-dimensional finite element computational procedure is developed for the accurate analysis of the strains and stresses in adhesively bonded joints, and a delayed failure criterion based on the Reiner-Weisenberg failure theory has also been implemented in the finite element code.

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64 citations

"Numerical finite element formulatio..." refers methods in this paper

...Roy and Reddy [5] used a similar integration approach to Henriksen’s and formulated a numerical integration method for the Schapery non-linear viscoelastic model coupled with moisture sorption and used for 2D FE modelling of adhesively bonded joints....
[...]

Journal Article•DOI•

The Nonlinear Thermoviscoelastic Characterizations of FM‐73 Adhesives

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D. Peretz, Y. Weitsman

01 Apr 1983-Journal of Rheology

TL;DR: In this article, an experimental investigation of the response of "neat,” unscrimmed FM-73 adhesive under mechanical loads at various stress levels and over the 30-60°C temperature range is presented.

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Abstract: This work presents an experimental investigation of the response of “neat,” unscrimmed FM‐73 adhesive under mechanical loads at various stress levels and over the 30–60°C temperature range The methodically acquired data provide the basis for a material characterization based on a specific model of nonlinear viscoelastic response In particular, it is shown that it is essential to include transient‐temperature testing in the characterization scheme Subsequent tests were performed under conditions of fluctuating loads and temperatures in order to verify the predictive capabilities of the model and characterization scheme Satisfactory results were obtained

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50 citations