Thermodynamics, stability and nonlinear oscillations of a viscoelastic solid Part 1:Differential type solids of second grade
by
R.L. Fosdick and J.-H. Yu
in
Int. J. Nonlinear Mech., 31, 495-516, 1996.
Category: Journal Article
Keywords: thermodynamics; viscoelastic solids; stability
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Abstract:
We study the thermodynamics and stability of a viscoelastic second grade solid whose action is characterized by two microstructural coefficients α1 and α2 in addition to the Newtonian viscosity μ. We show that it is both necessary and sufficient that μ greater-or-equal, slanted 0, α1 greater-or-equal, slanted 0 and α1 + α2 = 0 if the material model is to be compatible with thermodynamics and its free energy is to be at a local minimum in equilibrium. Then, we construct a stability theorem for second grade solids which undergo mechanically isolated motions wherein it is shown that the motion of the body relative to its center of mass will dissipate away in time. The stability theorem is exemplified by investigating the free oscillation of cylindrical and spherical shells where the equilibrium state is globally stable. When μ = 0, but α1 ≠ 0, the shells exhibit a larger period than if they were purely elastic in the classical sense.
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