Approximate contact force model for viscoelastic materials based on generalized Maxwell model

Ding, Suhang; Hu, Yiqun; Jian, Bin; Zhang, Yuhang; Su, Lei; Xia, Re; Hu, Guoming

doi:10.1016/j.ijsolstr.2024.112645

Cited by 3 publications

(3 citation statements)

References 34 publications

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“…The generalized Maxwell model expands on this by incorporating multiple Maxwell elements in parallel with an ideal spring. In the generalized Maxwell model [ 27 ], after applying Fourier transformation to the stress( σ )–strain( ε ) relationship, the shear storage modulus

, and shear loss modulus

can be defined by specific formulas:

where

is the elastic modulus,

is the frequency, and

(

= 1, 2 … N ) and

( i = 1, 2 … N ) are the elastic modulus and damping in each elastic element, respectively. The equations could not be used directly with commercial software [ 28 ].…”

Section: Modelingmentioning

confidence: 99%

“…The generalized Maxwell model expands on this by incorporating multiple Maxwell elements in parallel with an ideal spring. In the generalized Maxwell model [27], after applying Fourier transformation to the stress(σ)-strain(ε) relationship, the shear storage modulus G s (ω), and shear loss modulus G L (ω) can be defined by specific formulas:…”

Section: Generalized Maxwell Modelmentioning

confidence: 99%

See 1 more Smart Citation

The Frictional Vibration Attenuation of Rubber Utilizing a Groove on the Body

Qu,

Wang,

Ren

et al. 2024

Polymers

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Frictionally induced vibrations in rubber are readily triggered due to their lower stiffness and higher elasticity. This study developed a numerical model to investigate the frictional vibration of a rubber block with a groove on its side surface against an aluminum disc. The results indicate that a backside groove (GB) on the block significantly enhances vibration attenuation, with a decay time 0.6 s faster than a non-grooved (NG) block, despite a potentially higher initial vibrational amplitude. In contrast, a frontside groove (GF) results in persistent frictional oscillations, with the steady-state time being similar for both GB and GF configurations. The underlying mechanism is attributed to the GB’s effectiveness in reducing the maximum energy imparted to the block initially, dissipating vibrational energy more swiftly, and distributing the contact stress more uniformly. The discrepancies in frictional forces between the conducted experiment and the simulation for the NG, GB and GF cases were 11.3%, 9.3% and 12.1%, respectively, quantitatively indicating the moderate precision of the results from the simulation. The insights gained from this study hold promise for enriching methods of mitigating vibrations arising from rubber friction.

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, and shear loss modulus

can be defined by specific formulas:

where

is the elastic modulus,

is the frequency, and

(

= 1, 2 … N ) and

( i = 1, 2 … N ) are the elastic modulus and damping in each elastic element, respectively. The equations could not be used directly with commercial software [ 28 ].…”

Section: Modelingmentioning

confidence: 99%

“…The generalized Maxwell model expands on this by incorporating multiple Maxwell elements in parallel with an ideal spring. In the generalized Maxwell model [27], after applying Fourier transformation to the stress(σ)-strain(ε) relationship, the shear storage modulus G s (ω), and shear loss modulus G L (ω) can be defined by specific formulas:…”

Section: Generalized Maxwell Modelmentioning

confidence: 99%

The Frictional Vibration Attenuation of Rubber Utilizing a Groove on the Body

Qu,

Wang,

Ren

et al. 2024

Polymers

View full text Add to dashboard Cite

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“…A close examination of recently published articles reveals many interested in the modeling of transient behavior in viscoelastic finite elements. Many employ these common constitutive relations and often use a step-wise integration scheme, such as the Newmark-Beta method [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

A generalized time-domain constitutive finite element approach for viscoelastic materials

Abercrombie,

Gregory McDaniel,

Walsh

2024

Modelling Simul. Mater. Sci. Eng.

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Despite the existence of time domain finite element formulations forviscoelastic materials, there are still substantial ways to improve the analysis. Tothe authors’ knowledge, the formulation of the problem is always done with respectto a single constitutive relation and so limits the implementer to a single scheme withwhich to model relaxation. Furthermore, all current constitutive relations involvethe finding of fitting parameters for an analytical function, which is a sufficientlypainful process to warrant the study of best fitting procedures to this day. Incontrast, this effort is the first full derivation of the two dimensional problem fromfundamental principles. It is also the first generalization of the problem, which freesusers to select constitutive relations without re-derivation or re-expression of theproblem. This approach is also the first approach to the problem that could leadto the elimination of constitutive relations for representing relaxation in viscoelasticmaterials. Following, the full derivation, several common constitutive relations areoutlined with analysis of how they may best be implemented in the generalized form.Several expressions for viscoelastic terms are also provided given linear, quadratic, andexponential interpolation assumptions.

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