Theoretical and numerical aspects in weak-compressible finite strain thermo-elasticity

• Autorzy: Hamkar A.-W. , Hartmann S.

Warianty tytułu

PL

Teoretyczne i numeryczne aspekty słabo ściśliwego sformułowania termosprężystości dużych deformacji

• Języki publikacji: EN

Abstrakty

EN

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.

PL

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

EN

thermoelasticity; finite strains; finite elements; Rosenbrock--type methods

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2012
• Tom: Vol. 50 nr 1
• Strony: 3--22
• Opis fizyczny: Bibliogr. 31poz., rys.

Twórcy

autor

Hamkar A.-W.

autor

Hartmann S.

• Clausthal University of Technology, Institute of Applied Mechanics, Clausthal-Zellerfeld, Germany,

Bibliografia

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