Multiscale considerations in modeling of nonlinear elastomers

International Journal for Computational Methods in Engineering Science and Mechanics

Volumn 8, Issue 2, 2007, Pages 53-62

  Banks, H T ^a   Medhin, Negash G ^a   Pinter, Gabriella A ^b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Computational methods; Hysteresis; Molecular dynamics; Multiscale modeling; Nonlinear partial differential equations; Viscoelasticity

Indexed keywords

COMPUTATIONAL METHODS; HYSTERESIS; MATHEMATICAL MODELS; MOLECULAR DYNAMICS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; RUBBER; VISCOELASTICITY;

MULTISCALE MODELING; NONLINEAR ELASTOMERS; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS;

ELASTOMERS;

EID: 33847163593     PISSN: 15502287     EISSN: 15502295     Source Type: Journal    
DOI: 10.1080/15502280601149346     Document Type: Article

References (36)

1. Banks, H. T., Smith, R. C., and Wang, Y., Smart Material Structures: Modeling, Estimation and Control, MassOn, Paris and John Wiley and Sons, Chichester (1996).
2. Gandhi, M. V., and Thompson, B. S., Smart Materials and Structures, Chapman and Hall, London (1992).
3. Doi, M., and Edwards, M., The Theory of Polymer Dynamics, Oxford, New York (1986).
4. Johnson, A. R., and Stacer, R. G., "Rubber viscoelasticity using the physically constrained systems' stretches as internal variables," Rubber Chem. Tech. 66, 567-577 (1993).
5. Banks, H. T., Medhin, N. G., and Pinter, G. A., "Nonlinear reptation in molecular based hysteresis models for polymers," Quarterly of Applied Mathematics 62(4), 767-779 (2004).
6. Christensen, R. M., Theory of Viscoelasticity: An Introduction, 2nd ed., Academic Press, New York (1982).
7. Findley, W. N., Lai, J. S., and Onaran, K., Creep and Relaxation of Nonlinear Viscoelastic Materials, North-Holland Series in Applied Mathematics and Mechanics, North-Holland Publishing Company, Amsterdam (1976).
8. Ferry, J. D., Viscoelastic Properties of Polymers, John Wiley & Sons, New York (1980).
9. Ogden, R. W., Non-Linear Elastic Deformations, Ellis Horwood Limited, Chichester (1984).
10. Rivlin, R. S., "Large elastic deformations of isotropic materials, I, II, III," Phil. Trans. Roy. Soc: A 240, 459-525 (1948).
11. Schapery, R. A., "On the characterization of nonlinear viscoelastic materials," Polymer Engineering and Science 9, 295-310 (1969).
12. Banks, H. T., and Lybeck, N., "Modeling methodology for elastomer dynamics," in Systems and Control in the 21st Century, (C. Byrnes, et al., eds.), Birkhäuser, Boston, 37-50 (1996).
13. Banks, H. T., Lybeck, N. J., Gaitens, M. J., Muñoz, B. C., and Yanyo, L. C. "Computational methods for estimation in the modeling of nonlinear elastomers," CRSC-TR95-40, NCSU, December 1995;
14. Kybernetika 32, 526-542 (1996).
15. Banks, H. T., Gilliam, D. S., and Shubov, V. I., "Global solvability for damped abstract nonlinear hyperbolic systems," Differential and Integral Equations 10, 309-332 (1997).
16. Banks, H. T., and Pinter, G. A., "Approximation results for parameter estimation in nonlinear elastomers," CRSC-TR96-34, NCSU, December 1996;
17. Control and Estimation of Distributed Parameter Systems (F. Kappel, et al., eds.), Birkhäuser, Boston, 1-13 (1998).
18. Banks, H. T., and Pinter, G. A., "Damping: hysteretic damping and models," CRSC-TR99-36, NCSU, December 1999;
19. Encyclopedia of Vibrations, Academic Press, London, 658-664 (2001).
20. Lesieutre, G. A., "Modeling frequency-dependent longitudinal dynamic behavior of linear viscoelastic long fiber components," J. Composite Materials 28, 1770-1782 (1994).
21. Lesieutre, G. A., and Govindswamy, K., "Finite element modeling of frequency-dependent and temperature-dependent dynamic behavior of viscoelastic materials in simple shear," Int. J. Solids Structures 33, 419-432 (1996).
22. Johnson, A. R., Quigley C. J., and Mead, J. L., "Large strain viscoelastic constitutive models for rubber, part I: Formulations," Rubber Chemistry Technology 67, 904-917 (1994).
23. Banks, H. T., Pintér, G. A., and Potter, L. K., "Existence of unique weak solutions to a dynamical system for nonlinear elastomers with hysteresis," CRSC-TR98-43, NCSU, November 1998;
24. Differential and Integral Equations 13, 1001-1024 (2000).
25. Banks, H. T., Pintér, G. A., Potter, L. K., Gaitens, M. J., and Yanyo, L. C., "Modeling of nonlinear hysteresis in elastomers under uniaxial tension," J. Intelligent Material Systems and Structures 10, 116-134 (1999).
26. Zhang, Y., Mathematical Formulation of Vibrations of a Composite Curved Beam Structure: Aluminum Core Material with Viscoelastic Layers, Constraining Layers and Piezoceramic Patches, Ph.D. Thesis, N.C. State University, May 1997.
27. Ackleh, A. C., Banks, H. T., and Pinter, G. A., "Well-posedness results for models of elastomers," J. Math. Analysis and Applications 268, 440-456 (2002).
28. Dautray, R., and Lions, J. L., Mathematical Analysis and Numerical Methods for Science and Technology, Volume 5, Evolution Problems I, Springer, New York (2000).
29. Ha, J., and Nakagiri, S., "Existence and regularity of weak solutions for semilinear second order evolution equations," Funkcialaj Ekvacioj 41, 1-24 (1998).
30. Ackleh, A. C., Banks, H. T., and Pinter, G. A., "On a nonlinear beam equation," Applied Math. Letters 15, 381-387 (2002).
31. Banks, H. T., and Medhin, N. G., "A molecular based dynamic model for viscoelastic responses of rubber in tensile deformations," CRSC-TROO-27, NCSU, October, 2000;
32. Communications on Applied Nonlinear Analysis 8, 1-18 (2001).
33. Banks, H. T., and Bihari, K., "Modeling and estimating uncertainty in parameter estimation," CRSC-TR99-40, NCSU, December 1999;
34. Inverse Problems 17, 1-17 (2001).
35. Banks, H. T., Bortz, D., Pinter, G. A., and Potter, L. K., "Modeling and imaging techniques with potential application in bioterrorism," CRSC-TR03-02, NCSU, January 2003;
36. Chapter 6 in Bioterrorism: Mathematical Modeling Applications in Homeland Security (H. T. Banks and C. Castillo-Chavez, eds.), Frontiers in Applied Mathematics, Vol. 28, SIAM, Philadelphia, 129-154 (2003).