Thermodynamics, stability and nonlinear oscillations of viscoelastic solids. II: History type solids
[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.
exponentially decaying relaxation function
free radial motion of cylindrical and spherical shells
scientific article; zbMATH DE number 1063931
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