On the null condition for nonlinearly elastic solids

• Autorzy: Domański W. , Ogden R. W.
• Konferencja: International Conference on Continuous and Discrete Modelling in Mechanics (05-09.09.2005 ; Warsaw ; Poland)
• Języki publikacji: EN

Abstrakty

EN

Smooth solutions to the Cauchy problem for the equations of nonlinear elastodynamics exist typically only locally in time. However, under the assumption of small initial data and an additional restriction, the so-called null condition, global existence and uniqueness of a classical solution can be proved. In this paper, we examine this condition for the elastodynamic equations and study its connection with the property of genuine nonlinearity as well as its relation with the phenomenon of self-resonance of nonlinear elastic waves. Using a special structure of plane waves elastodynamics [13], we provide an alternative and simple formulation of the null condition. This condition is then evaluated for some examples of elastic constitutive laws in order to determine the nature of the restrictions that it imposes.

Słowa kluczowe

EN

nonlineary elastic solid; Cauchy problem; null condition; elastodynamics; Murnaghan material; St. Venant-Kirchhoff material

PL

nieliniowo sprężyste ciała stałe; zagadnienie Cauchy'ego; stan zerowy; materiał Murnaghana; materiał St. Venant'a-Kirchohoff'a

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2006
• Tom: Vol. 58, nr 4-5
• Strony: 339--361
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Domański W.

autor

Ogden R. W.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland,

Bibliografia

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