A viscoelastic-viscoplastic constitutive model and its finite element implementation of amorphous polymers

Liang, Zhihong; Li, Jian; Zhang, Xuelian; Kan, Qianhua

doi:10.1016/j.polymertesting.2022.107831

Cited by 16 publications

(8 citation statements)

References 56 publications

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“…Let G 2 , defined by (20), be the set of the fractional Maxwell model admissible parameters with equal parametersα and β. Then, the relaxation modulus G M (t, g) (10) of the model ( 9) is continuous and differentiable with respect to g (8) for any time t ∈ T and sup t∈T ,g∈G 2…”

Section: Lipschitz Continuity Of Fmm With Respect To Model Parametersmentioning

confidence: 99%

“…Since, for any t ∈ T function, G M (t, g) (10) is differentiable with respect to g and in this case β = α, the four-element vector of model parameters g (8) is as follows…”

Section: Conflicts Of Interestmentioning

confidence: 99%

“…In addition to theoretical research dedicated to fractional-order rheological models [1][2][3][4][5], hundreds of studies have been conducted on the applicability of such models for specific materials to describe their mechanical properties. The applicability of such models to the description of different polymers is well known, for example, poly-isobutylene [4], polyurea and PET [6], shape memory polymers [7], amorphous polymers [8] and flax fiber-reinforced polymer [9]. Fractional viscoelastic models are also used for modeling laminated glass beams in the pre-crack state under explosive loads [10]; stress relaxation behavior of glassy polymers [11]; description of fiber-reinforced rubber concrete [12]; viscoelastic modeling of modified asphalt mastics [13]; and modeling rate-dependent nonlinear behaviors of rubber polymers [14].…”

Section: Introductionmentioning

confidence: 99%

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Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Stankiewicz

2024

Materials

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Considerable development has been observed in the area of applying fractional-order rheological models to describe the viscoelastic properties of miscellaneous materials in the last few decades together with the increasingly stronger adoption of fractional calculus. The fractional Maxwell model is the best-known non-integer-order rheological model. A weighted least-square approximation problem of the relaxation modulus by the fractional Maxwell model is considered when only the time measurements of the relaxation modulus corrupted by additive noises are accessible for identification. This study was dedicated to the determination of the model, optimal in the sense of the integral square weighted model quality index, which does not depend on the particular sampling points applied in the stress relaxation experiment. It is proved that even when the real description of the material relaxation modulus is entirely unknown, the optimal fractional Maxwell model parameters can be recovered from the relaxation modulus measurements recorded for sampling time points selected randomly according to respective randomization. The identified model is a strongly consistent estimate of the desired optimal model. The exponential convergence rate is demonstrated both by the stochastic convergence analysis and by the numerical studies. A simple scheme for the optimal model identification is given. Numerical studies are presented for the materials described by the short relaxation times of the unimodal Gauss-like relaxation spectrum and the long relaxation times of the Baumgaertel, Schausberger and Winter spectrum. These studies have shown that the appropriate randomization introduced in the selection of sampling points guarantees that the sequence of the optimal fractional Maxwell model parameters asymptotically converge to parameters independent of these sampling points. The robustness of the identified model to the measurement disturbances was demonstrated by analytical analysis and numerical studies.

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Section: Lipschitz Continuity Of Fmm With Respect To Model Parametersmentioning

confidence: 99%

“…Since, for any t ∈ T function, G M (t, g) (10) is differentiable with respect to g and in this case β = α, the four-element vector of model parameters g (8) is as follows…”

Section: Conflicts Of Interestmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Stankiewicz

2024

Materials

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“…Payne et al [24] assumed that the displacement dependence of the material was mainly due to the influence of the micro filler network system, and used the Kraus model to explain the correlation characteristics between dynamic properties of the damper and displacement amplitudes. Liang et al [25] built a constitutive model of viscoelastic materials based on a complex combination of multiple relaxation viscoelastic and viscoplastic models, which can predict the remarkable temperature-and rate-dependent deformation behaviors of materials well. Bagley et al [26] and Lewandowski [27] investigated the mechanical behavior of viscoelastic materials and conducted a structural seismic analysis of damping structures based on fractional derivative theory, which has a more concise form and higher accuracy than integral derivative models.…”

Section: Introductionmentioning

confidence: 99%

Experimental and Theoretical Investigation of Viscoelastic Damper by Applying Fractional Derivative Method and Internal Variable Theory

Guo

et al. 2023

Buildings

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Viscoelastic dampers are conventional passive vibration control devices with excellent energy dissipation performance. The fractional derivative has a simple form and high accuracy in the modelling of viscoelastic materials/dampers. The internal variables reflect the internal state evolution of materials, and are often used to analyze the deformation and thermal process of materials. In the present work, the mechanical properties of a plate-shear-type viscoelastic damper at room temperature are tested under sinusoidal displacement excitations. The impacts of frequency and displacement amplitude on the dynamic properties of the viscoelastic damper in a wide frequency domain (0.1–25 Hz) are investigated. The higher-order fractional derivative model and the temperature–frequency equivalent principle are employed to characterize the frequency and temperature influence, and the internal variable theory considering the internal/microscale structure evolutions is introduced to capture the displacement affection. The higher-order fractional derivative model modified with the internal variable theory and temperature–frequency equivalent principle (ITHF) is accurate enough in describing the dynamic behaviors of viscoelastic dampers with varying frequencies and displacement amplitudes.

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“…For polymers, different cruciform-designed specimens are used for biaxial tensile testing, which also requires a specialized test rig [22]. It is relevant to mention that in addition to the above-mentioned elastoplastic constitutive modeling approach for polymers, there are other anisotropic viscoelastic-viscoplastic models that have been successfully implemented in many studies [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Simplified Characterization of Anisotropic Yield Criteria for an Injection-Molded Polymer Material

Shahid,

Andreasson,

Petersson

et al. 2023

Polymers

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Injection-molded polyethylene plates exhibit highly anisotropic mechanical behavior due to, e.g., the uneven orientation of the polymer chains during the molding process and the differential cooling, especially in the thickness direction. Elastoplastic finite element modeling of these plates in particular is used with isotropic yield criteria like von Mises, trading off accuracy in favor of simpler constitutive characterization and faster solution. This article studies three different anisotropic yield criteria, namely, Hill 1948, Barlat Yld91, and Barlat Yld2004-18P, for the finite element modeling of low-density polyethylene (LDPE) at large uniaxial tensile deformation and compares the accuracy and computation time with von Mises. A simplified calibration technique is investigated to identify the constitutive parameters of the studied Barlat group yield criteria. The calibration process is simplified in the sense that only uniaxial tensile tests with digital image correlation measurements are used for the calibration of all the yield criteria studied in this article, although a standard calibration procedure for the Barlat group yield criteria requires additional material testing using more demanding test setups. It is concluded that both Barlat Yld91 and Barlat Yld2004-18P yield criteria can be calibrated with only a few tensile tests and still capture anisotropy in deformation–stress–strain at different levels of accuracy.

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A viscoelastic-viscoplastic constitutive model and its finite element implementation of amorphous polymers

Cited by 16 publications

References 56 publications

Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Experimental and Theoretical Investigation of Viscoelastic Damper by Applying Fractional Derivative Method and Internal Variable Theory

Simplified Characterization of Anisotropic Yield Criteria for an Injection-Molded Polymer Material

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