Thermodynamics, stability and nonlinear oscillations of viscoelastic solids. II: History type solids
type: Item
instance of: scholarly article
title: Thermodynamics, stability and nonlinear oscillations of viscoelastic solids. II: History type solids
zbMATH Open document ID: 0891.73026
DOI: 10.1016/S0020-7462(96)00146-1
author: Jang-Horng Yu
author: Roger Fosdick
published in: International Journal of Non-Linear Mechanics
publication date: 1997-09-21T00:00:00Z
review text: [For part I see the authors, ibid. 31, No. 4, 495-516 (1996; Zbl 0859.73008).] We study the thermodynamics and stability of a history type viscoelastic solid with an exponentially decaying relaxation function. The relaxation modulus must be nonnegative, and the Helmholtz free energy must be at a minimum at equilibrium in order for the material model to be compatible with thermodynamics. We construct a stability theorem for a history type solid which undergoes mechanically isolated motions by showing that the intrinsic motion of the body with respect to the center of mass is stable in the sense of Lyapunov. We then exemplify this stability theorem by studying the free radial motion of cylindrical and spherical shells through the construction of a history dependent Lyapunov functional. Numerical simulation indicate that the equilibrium state is globally stable.
Mathematics Subject Classification ID: 74D05
Mathematics Subject Classification ID: 74D10
Mathematics Subject Classification ID: 74A15
zbMATH DE Number: 1063931
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: Newtonian viscous solids
zbMATH Keywords: exponentially decaying relaxation function
zbMATH Keywords: Helmholtz free energy
zbMATH Keywords: free radial motion of cylindrical and spherical shells
zbMATH Keywords: history dependent Lyapunov functional
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1063931