Identyfikatory
Warianty tytułu
Teoretyczne i numeryczne aspekty słabo ściśliwego sformułowania termosprężystości dużych deformacji
Języki publikacji
Abstrakty
In this essay, a constitutive model for nearly incompressible elastic behavior is extended to the case to thermal effects. First, the use is made of the multiplicative decomposition of the deformation gradient into a thermal and a mechanical part. The thermal part is purely volumetric. Additionally, the mechanical part is multiplicatively decomposed into a volume-preserving and a volume-changing part so that the final stress state shows the influences of the temperature-dependence. The proposed model is carefully studied in view of the thermo-mechanical coupling effects. Second, the model is implemented into a time-adaptive finite element formulation based on higher-order Rosenbrock-type methods, which is a completely iteration-free procedure so that really fast computations are available. The article concludes with a three-dimensional numerical simulation of a representative elastomeric tensile specimen.
W pracy przedstawiono model niemal nieściśliwego, sprężystego zachowania się materiału, rozszerzając go na efekty termiczne. Na początku rozważań dokonano multiplikatywnej dekompozycji gradientu deformacji na część termiczną i mechaniczną. Część termiczna wykazuje charakter czysto objętościowy. Dodatkowo, część mechaniczną zdekomponowano na element zachowujący objętość i element o zmiennej objętości w ten sposób, że wypadkowy stan naprężeń wykazuje wrażliwość na temperaturę. Zaproponowany model szczegółowo zbadano w kontekście efektów sprzężenia termomechanicznego. W dalszej części pracy, analizowany model zastosowano do czasowo adaptacyjnej metody elementów skończonych sformułowanej na podstawie metod Rosenbrocka wyższych rzędów. Takie sformułowanie umożliwia uzyskanie procedury beziteracyjnej, co z kolei pozwala na wykonanie wyjątkowo szybkich obliczeń numerycznych. Artykuł zamyka przykład symulacji numerycznej trójwymiarowej próbki elastomeru poddanej próbie rozciągania.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
3--22
Opis fizyczny
Bibliogr. 31poz., rys.
Twórcy
autor
autor
- Clausthal University of Technology, Institute of Applied Mechanics, Clausthal-Zellerfeld, Germany, stefan.hartmann@tu-clausthal.de
Bibliografia
- 1. Ehlers W., Eipper G., 1998, The simple tension problem at large volumetric strains computed from finite hyperelastic material laws, Acta Mechanica, 130, 17-27
- 2. Flory P.J., 1961, Thermodynamic relations for high elastic materials, Transaction of the Faraday Society, 57, 829-838
- 3. Gear C.W., 1986, Maintaining solution invariants in the numerical solution of ODEs, SIAM Journal on Scientific and Statistical Computing, 7, 3, 734-743
- 4. Hairer E., Wanner G., 1996, Solving Ordinary Differential Equations II, Springer, Berlin, 2nd revised edition
- 5. Hartmann S., 2001a, Numerical studies on the identification of the material parameters of Rivlin’s hyperelasticity using tension-torsion tests, Acta Mechanica, 148, 129-155
- 6. Hartmann S., 2001b, Parameter estimation of hyperelasticity relations of generalized polynomial-type with constraint conditions, International Journal of Solids and Structures, 38, 44/45, 7999-8018
- 7. Hartmann S., 2002, Computation in finite strain viscoelasticity: finite elements based on the interpretation as differential-algebraic equations, Computer Methods in Applied Mechanics and Engineering, 191, 13/14, 1439-1470
- 8. Hartmann S., Hamkar A.-W., 2010, Rosenbrock-type methods applied to finite element computations within finite strain viscoelasticity, Computer Methods in Applied Mechanics and Engineering, 199, 23/24, 1455-1470
- 9. Hartmann S., Neff P., 2003, Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility, International Journal of Solids and Structures, 40, 11, 2767-2791
- 10. Hartmann S., Quint K.J., Hamkar, A.-W., 2008, Displacement control in time-adaptive non-linear finite-element analysis, Journal of Applied Mathematics and Mechanics, 88, 5, 342-364
- 11. Hartmann S., Wensch J., 2007, Finite element analysis of viscoelastic structures using Rosenbrock-type methods, Computational Mechanics, 40, 383-398
- 12. Haupt P., 1985, On the concept of an intermediate configuration and its application to representation of viscoelastic-plastic material behavior, International Journal of Plasticity, 1, 303-316
- 13. Haupt P., 2002, Continuum Mechanics and Theory of Materials, Springer, Berlin, 2 edition
- 14. Haupt P., Tsakmakis C., 1989, On the application of dual variables in continuum mechanics, Journal of Continuum Mechanics and Thermodynamics, 1,165-196
- 15. Haupt P., Tsakmakis C., 1996, Stress tensors associated with deformation tensors via duality, Archive of Mechanics, 48, 347-384
- 16. Heimes T., 2005, Finite Thermoinelastizit¨at, Number 709 in Fortschrittsberichte, Reihe 5, Grund- und Werkstoffe/Kunststoffe, VDI-Verlag, D¨usseldorf
- 17. Holzapfel G., Simo J., 1996a, A new viscoelastic constitutive model for continuous media at finite thermomechanical changes, International Journal of Solids and Structures, 33, 3019-3034
- 18. Holzapfel G., Simo J., 1996b, Entropy elasticity of isotropic rubber-like solids at finite strains, Computer Methods in Applied Mechanics and Engineering, 132, 17-44
- 19. Lang J., 2000, Adaptive multilevel solution of nonlinear parabolic PDE systems. Theory, algorithm, and applications, Springer, Berlin
- 20. Lion A., 1997, A physically based method to represent the thermomechanical behaviour of elastomers, Acta Mechanica, 123, 1-26
- 21. Lion A., 2000, Thermomechanik von Elastomeren. Experimente und Materialtheorie, Habilitation, Institute of Mechanics, University of Kassel, Report No. 1/2000
- 22. Lu S., Pister K., 1975, Decomposition of deformation and representation of the free energy function for isotropic thermoelastic solids, International Journal of Solids and Structures, 11, 927-934
- 23. Lubich C., Roche M., 1990, Rosenbrock methods for differential-algebraic systems with solution-dependent singular matrix multiplying the derivative, Computing, 43, 325-342
- 24. Miehe C., 1988, Zur numerischen Behandlung thermomechanischer Prozesse, Report No. F88/6, University of Hannover, Institut f¨ur Baumechanik Und Numerische Mechanik
- 25. Miehe C., 1995, Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation, Computer Methods in Applied Mechanics and Engineering, 120, 243-269
- 26. Rang J., Angermann L., 2008, New Rosenbrock methods of order 3 for PDAEs of index 2, Advances in Differential Equations and Control Processes, 1, 2, 193-217
- 27. Reese S., 2001, Thermomechanische Modellierung gummiartiger Polymer-Strukturen, Habilitation, Institut f¨ur Baumechanik und Numerische Mechanik, Universit¨at Hannover, Report No. F01/4
- 28. Simo J.C., Miehe C., 1992, Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Computer Methods in Applied Mechanics and Engineering, 98, 41-104
- 29. Simo J.C., Taylor R.L., 1991, Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms, Computer Methods in Applied Mechanics and Engineering, 85, 273-310
- 30. Simo J.C., Taylor R.L., Pister K.S., 1985, Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Computer Methods in Applied Mechanics and Engineering, 51, 177-208
- 31. Treloar L.R.G., 1975, The Physics of Rubber Elasticity, Clarendon Press, Oxford, 3rd edition
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWM6-0010-0035