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Thermo-hyper-viscoelastic analysis of a rubber cylinder under cyclic deformation

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Abstract

In the present work, analysis of the thermal behavior of a rubber cylinder under the repeated deformation is studied. This problem is divided into two correlated parts including transient thermal heat conduction and cyclic mechanical loading. To find the best approach-numerical method, the problem is modeled and analyzed by three approaches including coupled approach-FEM, uncoupled approach-FEM as well as Green’s function. To evaluate the dissipating energy due to hysteresis, the Prony–Mooney–Rivlin constitutive hyper-viscoelastic mathematical model is considered. To model the thermal effects and heat buildup due to dissipating energy, this energy is accounted for as a heat source inside the part in three different forms including pointwise, planar, and volumetric. It is shown that the FEM-based coupled approach presents the most accurate estimation. However, for steady-state estimation of mid-point and wall-point temperatures, the best method is Green’s function with the planar and the volumetric heat source assumptions. Moreover, a study on the effect of frequency of loading cycles in temperature distribution shows that the more the frequency, the larger the difference between the temperature of the mid-point and wall-point, and the higher maximum temperature inside the rubber.

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Abbreviations

w :

Stored strain energy function

Q :

Dissipated energy

σ v :

The rate-dependent stress

σ h :

Hyperelastic stress

δ :

Loss angle

E* :

Complex modulus

E′:

Storage modulus

E″:

Loss modulus

I i :

Invariants of Cauchy–Green strain tensor

J :

Jacobian

E ∞ :

Long-term modulus

E i :

Relaxation modulus

θ i :

Relaxation time

C pq :

Model parameters

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, 61357-43337, Ahvaz, Iran

    Amirheshmat Khedmati Bazkiaei, Kourosh Heidari Shirazi & Mohammad Shishesaz

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  1. Amirheshmat Khedmati Bazkiaei
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  2. Kourosh Heidari Shirazi
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  3. Mohammad Shishesaz
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Correspondence to Kourosh Heidari Shirazi.

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Appendix A

Appendix A

Experimental tests and mechanical properties of rubber–metal and Caoutchouc–butyl rubber (Tables 5 and 6 ).

Table 5 Experimental tests results of Caoutchouc–butyl rubber with 40% carbon black [34]
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Table 6 Heat properties of the rubber–metal [35]
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Bazkiaei, A.K., Shirazi, K.H. & Shishesaz, M. Thermo-hyper-viscoelastic analysis of a rubber cylinder under cyclic deformation. J Rubber Res 24, 13–26 (2021). https://doi.org/10.1007/s42464-020-00068-2

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  • DOI: https://doi.org/10.1007/s42464-020-00068-2

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