On the nonlinear viscoelastic behavior of rubber-like materials: Constitutive description and identification

Tayeb, Adel; Arfaoui, Makrem; Zine, Abdelmalek; Hamdi, Adel; Benabdallah, Jalel; Ichchou, Mohamed

doi:10.1016/j.ijmecsci.2017.06.032

Cited by 26 publications

(11 citation statements)

References 37 publications

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“…The parameter estimation is important and the first step was done in the seminal work of Prony [120]. Several algorithms have been developed: graphically by log-log plots [32,127], least-squares method [54,144,149], nonlinear optimization methods [69], genetic-based algorithm [106], from the continuous relaxation time spectrum [17,79], logarithm equidistant distribution of relaxation times (known as the R-method) [76,79], quasi-linearization for multi-exponential decay curves fitting [50], etc.…”

Section: Discrete Relaxation Spectrum By Prony Series Decompositionmentioning

confidence: 99%

Response functions in linear viscoelastic constitutive equations and related fractional operators

Hristov

2019

Math. Model. Nat. Phenom.

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This study addresses the stress–strain relaxation functions of solid polymers in the framework of the linear viscoelasticity with aim to establish the adequate fractional operators emerging from the hereditary integrals. The analysis encompasses power-law and non-power-law materials, thus allowing to see the origins of application of the tools of the classical fractional calculus with singular memory kernels and the ideas leading towards fractional operators with non-singular (regular) kernels. A step ahead in modelling with hereditary integrals is the decomposition of non-power-law relaxation curves by Prony series, thus obtaining discrete relaxation kernels with a finite number of terms. This approach allows for seeing the physical background of the newly defined Caputo–Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories. The non-power-law relaxation curves also allow for approximations by the Mittag–Leffler function of one parameter that leads reasonably into stress–strain hereditary integrals in terms of Atangana–Baleanu fractional derivative of Caputo sense. The main outcomes of the analysis done are the demonstrated distinguishes between the relaxation curve behaviours of different materials and are therefore the adequate modelling with suitable fractional operators.

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Section: Discrete Relaxation Spectrum By Prony Series Decompositionmentioning

confidence: 99%

Response functions in linear viscoelastic constitutive equations and related fractional operators

Hristov

2019

Math. Model. Nat. Phenom.

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“…These models are either phenomenological or mechanistic. 6 The mechanical behavior of rubber compounds especially in analysis like RR simulation, where time scale is prominent, should be described by a viscoelastic model in conjunction with a hyperelastic equation for their time-independent behavior. Different approaches have been developed so far for the implementation of hyper-viscoelastic models in FE simulation of tires.…”

Section: Introductionmentioning

confidence: 99%

“…Different approaches have been developed so far for the implementation of hyper-viscoelastic models in FE simulation of tires. 6 Most of these approaches have been separately investigated, for their advantages and limitations. 7 However, to the best of our knowledge, there is lack of a comprehensive study on the applicability and accuracy of the FE simulation of tire RR using different viscoelastic models via comparison of the predicted results with experimental data.…”

Section: Introductionmentioning

confidence: 99%

Computer simulation of tire rolling resistance using finite element method: Effect of linear and nonlinear viscoelastic models

Rafei

Ghoreishy

Naderi

2018

Proceedings of the Institution of Mechanical Engineers, Part D:

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This research work is devoted to the study of the effect of model parameters and material properties on tire rolling resistance. The main goal of this research is to investigate and clarify the effect of the adopted hyper-viscoelastic material model on tire rolling resistance simulation results. For this purpose, some new approaches were used and current shortcomings were introduced. Computer simulations were carried out using Abaqus standard command line. Linear and parallel rheological framework viscoelastic models were implemented and rolling resistance of a passenger car tire was determined. Different parametric simulations were carried out and the results were compared with rolling resistance data obtained from experimental tests. The results revealed that the calculated rolling resistance force depends on the implemented viscoelastic model. The linear viscoelastic model could not accurately predict the trend of rolling resistance with variation of tire inflation pressure and applied load. On the contrary, parallel rheological framework could cope with this trend. The parallel rheological framework model is more sensitive to inflation pressure. However, the sensitivity of both models to applied vertical load is nearly the same. Although cornering simulation is independent of the adopted viscoelastic model, the type of viscoelastic model could affect the footprint contact pressure contour.

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“…The deformation gradient determinant and Green strain tensor are J ¼ detðFÞ and E ¼ 1 2 ðC À IÞ, respectively, where I is the identity matrix. For incompressible hyperelastic material, the Cauchy stress is given as follows in terms of the left Cauchy-Green deformation tensor invariants: [25][26][27]…”

Section: Hyperelasticitymentioning

confidence: 99%

Modeling hyperviscoelastic behavior of elastomeric materials (HDPE/POE blend) at different dynamic biaxial and uniaxial tensile strain rates by a new dynamic tensile-loading mechanism

Aligholizadeh

Yazdani

Sabouri

2019

Journal of Elastomers & Plastics

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This article presents a new model developed to investigate hyperviscoelastic behavior of elastomeric materials/polyolefin elastomers (HDPE/POE blend) under dynamic biaxial and uniaxial tensile loading. Various strain energy functions (SEF) have been used in this model, and their capability to predict hyperelastic behavior of the aforementioned materials was validated by experimental data. In the experimental part, a new dynamic tensile-loading mechanism was designed and developed to be mounted on a drop-weight impact-testing machine. As a novelty, this mechanism has the ability to perform either uniaxial or biaxial dynamic tensile tests for any type of material, especially for investigating the hyperviscoelastic behavior of materials like elastomers at various strain rates. In addition, a new hyperviscoelastic model has been developed for elastomeric material, which can predict the behavior of the material well at different strain rates. By increasing the strain rate in the dynamic biaxial and uniaxial loading, Pucci–Saccomandi and Yeoh SEF predicted the dynamic behavior of material well due to its lower root mean square error. In fact, in this case, these functions are more capable than Mooney–Rivlin, Neo-Hookean, and polynomial SEF in predicting the effect of the strain rates. In addition, the results show that Yeoh SEF performs much better than the other SEFs in predicting the material behavior in cases of dynamic biaxial and uniaxial tensile strain. The results also indicated that the newly designed mechanism was capable of performing dynamic tensile loading and extracting its accurate results and could reduce the cost of testing compared to other methods.

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On the nonlinear viscoelastic behavior of rubber-like materials: Constitutive description and identification

Cited by 26 publications

References 37 publications

Response functions in linear viscoelastic constitutive equations and related fractional operators

Response functions in linear viscoelastic constitutive equations and related fractional operators

Computer simulation of tire rolling resistance using finite element method: Effect of linear and nonlinear viscoelastic models

Modeling hyperviscoelastic behavior of elastomeric materials (HDPE/POE blend) at different dynamic biaxial and uniaxial tensile strain rates by a new dynamic tensile-loading mechanism

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