Numerical Modeling of Linear Viscoelasticity in a Finite Element Method Software Package to be Used in Multiphysics Modeling

علوم کاربردی و محاسباتی در مکانیک

Article 9, Volume 25, Issue 2, October 2014, Pages 121-131   

Document Type: مقاله کوتاه

DOI: 10.22067/fum-mech.v25i2.24850

Authors

Mojtaba Haghighi Yazdi^* ; Jafar Eskandari Jam

Abstract

In this paper, the capabilities of modeling linear viscoelasticty in a finite element method software package (COMSOL Multiphysics) have been investigated. The governing equations of linear viscoelasticity have been developed for 2D cases of plane stress and plane strain. These equations have been verified by solving a related engineering example. Since the developed equations are suitable for modeling multiphysics mechanisms, the presented model can also be used in modeling linear viscoleasticity coupled with other multiphysics phenomena.

Keywords

Numerical Method; Finite Element Modeling; Linear Viscoelasticity; Rheological Model; Multiphysics

References

1. Gasser, T. C. and Forsell, C., "The Numerical Implementation of Invariant-based Viscoelastic Formulations at Finite Strains. An Anisotropic Model for the Passive Myocardium", Computer Methods in Applied Mechanics and Engineering, Vol. 200(49-52), pp. 3637-3645, (2011).

2. COMSOL Multiphysics 4.0a, COMSOL Inc., (2005).

3. Moravec, F. and Letzelter, N., "On the Modeling of the Linear Viscoelastic Behaviour of Biological Materials Using Comsol Multiphysics", Applied and Computational Mechanics, Vol. 1, pp. 175-184, (2007).

4. Marvalova, B., "Application of COMSOL Multiphysics 3.2 to Finite Strain Viscoelasticity of an Elastomeric Solid", Proceedings of the COMSOL Users Conference, Prague, October, (2006).

5. Rambert, G., Grandidier, J.-C. and Cangemi, L., "A Modelling of the Coupled Thermodiffuso-Elastic Linear Behaviour. Application to Explosive Decompression of Polymers", Oil &Gas Science and Technology – Rev. IFP, Vol. 58(5), pp. 571-591, (2003).

6. Rambert, G. and Grandidier, J.-C., "An Approach to the Coupled Behaviour of Polymers Subjected to a Thermo-Mechanical Loading in a Gaseous Environment", European Journal of Mechanics A/Solids, Vol. 24, pp. 151-168, (2005).

7. Rambert, G., Jugla, G. and Grandidier, J.-C., "A Modelling of the Direct Couplings between Heat Transfer, Mass Transport, Chemical Reactions and Mechanical Behaviour. Numerical Implementation to Explosive Decomposition", Composites: Part A, Vol. 37, pp. 571-584, (2006).

8. Rambert, G., Grandidier, J.-C. and Aifantis, E.C., "On the Direct Interactions between Heat Transfer, Mass Transport and Chemical Processes within Gradient Elasticity", European Journal of Mechanics, A/Solids, Vol. 26(1), pp. 68-87, (2007).

9. Sorvari, J. and Malinen, M., "Numerical Interconversion between Linear Viscoelastic Material Functions with Regularization", International Journal of Solids and Structures, Vol. 44, pp.

1291–1303, (2007).

10. Wilkes, J.O., "Fluid Mechanics for Chemical Engineers with Microfluidics and CFD", 2nd Edition, Prentice Hall, N. J., (2005).

11. Zimmerman, W.B.J., "Multiphysics Modelling with Finite Element Methods", World Scientific Pub., London, Hackensack, N.J., (2006).

12. COMSOL Multiphysics User's Guide, COMSOL Multiphysics 4.0a Documentation, (2010).

13. Taylor, R.L., Pister, K.S. and Goudreau, G.L., "Thermomechanical Analysis of Viscoelastic Solids", International Journal for Numerical Methods in Engineering, Vol. 2(1), pp. 45-59, (1970).

14. Haghighi-Yazdi, M. and Lee-Sullivan, P., "Stress Relaxation of a Polycarbonate Blend after Hygrothermal Aging", Mechanics of Time-Dependent Materials, Vol. 17, pp. 171-193, (2013).

15. Guo, Y. and Bradshaw, R.D., "Isothermal Physical Aging Characterization of Polyether-Ether-Ketone (PEEK) and Polyphenylene Sulfide (PPS) Films by Creep and Stress", Mechanics of Time-Dependent Materials, Vol. 11(1), pp. 61-89, (2007).