Some energetic properties of smooth solutions in rate-type viscoelasticity. (English) Zbl 0553.73026

Some energetic properties of the smooth solutions of initial and boundary value problems in the semilinear rate-type theory of viscoelasticity are pointed out. The existence of a unique convex energy function having certain monotony properties with respect to the equilibrium curve is proved. For an isolated body the asymptotic approach to equilibrium (in the \(L_ 2\) sense) is shown. This property is used to obtain a rate-type viscoelasticity approach of nonlinear elasticity. Sufficient stability conditions are given for the solutions of the one-dimensional problem and for the three-dimensional problem with small strains.
Reviewer: Gh.Gr.Ciobanu


74Hxx Dynamical problems in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
74B20 Nonlinear elasticity
74S30 Other numerical methods in solid mechanics (MSC2010)


Zbl 0553.73027
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