On rate and gradient-dependence of solids as dynamical systems

• Autorzy: Beda P.
• Języki publikacji: EN

Abstrakty

EN

This paper aims at presenting a mathematical background of material instability problems such like strain localization or flutter, as an application of the theory of dynamical systems. The basic field equations of the solid continuum are the kinematic equations, the Cauchy equations of motion and the constitutive equations. This system of equations is completed with initial and boundary value conditions and can define a dynamical system. Then, a condition of material stability can be obtained using Lapunov's indirect method. Also the basic material instability modes can be classified as static (divergence type) or dynamic (Hopf) bifurcations of dynamical systems. Such formulation gives a mathematical interpretation of rate and gradient-dependence in the constitutive equations and mesh dependence in numerical studies, pointing out their close relationship to the structure of the critical eigenspace of an operator defined by the dynamical system.

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 1999
• Tom: Vol. 51, nr 3-4
• Strony: 229--241
• Opis fizyczny: Bibliogr. 20 poz.,

Twórcy

autor

Beda P.

• Research Group of the Dynamics of Machines and Vehicles, Technical University of Budapest, P.O. Box 91. H-1502 Budapest, Hungary