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

Lai, J.; Bakker, A.

doi:10.1007/s004660050138

Cited by 25 publications

(32 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Having analytically determined the values of g 0 and g 1 , then a s can be directly estimated by using equation (5). As De c and e vp can also be experimentally measured, a proper value of a s can be found by fitting the experimental values of the recovery response e r (t) in equation (5).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Equation (7) is numerically curve fitted to the linear recovery data, and the value of the n exponent is determined. The numerical estimation of a s can be performed by fitting the recovery data to the nondimensional formulation of equation (5). Knowing the values of a s and g 1 , the value of g 2 is analytically estimated using equation (17).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Several forms of the transient part of the creep compliance have been proposed. These forms include well established semiempirical representations like Findley's power law [1][2][3] and generalised power law 4 or mechanical analogues of springs and dashpots like Prony's exponential series [5][6][7] that are quite applicable in numerical implementation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effect of multiple step creep/creep recovery loading on non-linear viscoelastic response of carbon fibre reinforced polymers

Zaoutsos¹

2013

Plastics, Rubber and Composites

View full text Add to dashboard Cite

In the current study, the non-linear viscoelastic response of a polymer matrix composite under multiple creep/creep recovery loading has been investigated. Starting from Schapery's constitutive equation for the description of the non-linear viscoelastic response at single step loading, the influence of creep/creep recovery multiple step loading in the overall viscoelastic and viscoplastic strain responses is examined, and an attempt to model this behaviour is performed. Based on the modelling of the parameters of non-linearity, the effect of the number of creep/creep recovery cycles in the strain response is examined. It is evident that multiple creep/creep recovery loading has an impact on both viscoelastic and viscoplastic strain responses of polymers and their composites. Good to excellent agreement between the experimental data and the model values of the non-linear parameters is also very encouraging for the application of the model to the non-linear time dependent response of polymer composites.

show abstract

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effect of multiple step creep/creep recovery loading on non-linear viscoelastic response of carbon fibre reinforced polymers

Zaoutsos¹

2013

Plastics, Rubber and Composites

View full text Add to dashboard Cite

show abstract

“…For the present analysis, we utilize a viscoelastic material model based on the experimental findings of Lai and Bakker [1996] for a glassy amorphous polymer material (PMMA). The Prony series parameters for the viscoelastic relaxation modulus given in Table 1 were calculated by Payette and Reddy [2010] from the published compliance parameters [Lai and Bakker, 1996].…”

Section: Materials Propertiesmentioning

confidence: 99%

“…The Prony series parameters for the viscoelastic relaxation modulus given in Table 1 were calculated by Payette and Reddy [2010] from the published compliance parameters [Lai and Bakker, 1996]. Although the finite element formulation places no restriction on the relationship between E(t) and G(t), for the present analysis we adopt the approach taken by Chen [1995] and assume that the shear and relaxation moduli are related by…”

Section: Materials Propertiesmentioning

confidence: 99%

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

Vallala

Payette

Reddy

2012

Int. J. Appl. Mechanics

View full text Add to dashboard Cite

In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C 0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.which makes it more important to study these materials. The theory of viscoelastic behavior is long been established, the reader can refer to Lakes [2009] for a materials perspective and Reddy [2008], Flügge [1975], Christensen [1982], Findley et al. [1976] and Lockett [1975] for a continuum perspective. Within the continuum purview there are analytical methods like integral transforms, Laplace transforms and correspondence principle, etc., to study the mechanical response of structures made of viscoelastic materials. But as with many analytical methods, they are limited to simple cases of geometry and loading. In such scenarios numerical techniques like the finite element method becomes very useful in testing and predicting the properties of a material without actually fabricating them. Numerical methods can be used to obtain approximate solution with desired accuracy.Many researchers [Taylor et al., 1970;Oden and Armstrong, 1971;Holzapfel and Reiter, 1995;Henriksen, 1984;Hartmann, 2002;Roy and Reddy, 1988] have used the finite element method to study viscoelastic materials. The main difficulty with the viscoelastic finite element models is the approximation of convolution integrals that come from viscoelastic constitutive equations. Most of these finite element models try to circumvent the problem with the time-dependent convolution integrals by transforming them to a set of discrete algebraic equations in space. Taylor et al. [1970] and Oden and Armstrong [1971] used recurrence relations such that only the deformation history from last few iterations is needed to be stored instead of entire deformation from beginn...

show abstract

Investigation of the viscoelastic response of high temperature AS4‐12K/RP46 composites using a micromechanical approach

2014

View full text Add to dashboard Cite

The viscoelastic behavior of a RP46 polyimide resin is characterized at high temperature and the results are used within a micromechanical model to predict the viscoelastic response of a RP46 based carbon fiber composite. The creep master curve of the neat resin is obtained using the time temperature superposition principle (TTSP) from creep tests at three different temperatures, namely 180, 220, and 270 C. The viscoelastic behavior of RP46 is modeled based on Schapery's single integral constitutive equation whose Prony Series coefficients are obtained from the master curve. The acquired properties are then incorporated into a Simplified Unit Cell Micromechanical model to study the creep response of a RP46 resin based composite system. The advantage of this particular micromechanical model lies in its ability to give closed form expressions for the effective viscoelastic response of unidirectional composites as well as each of their constituents. Two types of nonlinearities were observed, one due to stress and the other due to temperature.

show abstract

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

Cited by 25 publications

References 0 publications

Effect of multiple step creep/creep recovery loading on non-linear viscoelastic response of carbon fibre reinforced polymers

Effect of multiple step creep/creep recovery loading on non-linear viscoelastic response of carbon fibre reinforced polymers

A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY

Investigation of the viscoelastic response of high temperature AS4‐12K/RP46 composites using a micromechanical approach

Contact Info

Product

Resources

About