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

Suliciu, I.

Int. J. Non-Linear Mech. 19, 525-544 (1984).

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

MSC:

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)

Keywords:

free energy function; second law of thermodynamics; energetic properties; smooth solutions; initial and boundary value problems; semilinear rate- type theory; existence; unique convex energy function; monotony properties; isolated body; asymptotic approach to equilibrium; Sufficient stability conditions; one-dimensional problem; three-dimensional problem with small strains

Citations:

Zbl 0553.73027