Global existence of solutions for the one-dimensional response of viscoelastic solids within the context of strain-limiting theory
This paper deals with the global existence of solutions for the one-dimensional response of viscoelastic solids within the context of the strain-limiting theory. Following the work of Rajagopal, for the strain-limiting model in the one-dimensional case and its extension to rate-type viscoelastic materials by proposing an implicit constitutive equation and including an additional term corresponding to linearized strain rate, the author discusses a constitutive relation which is a generalization of the Kelvin-Voigt viscoelastic model. This outlines the strength of this constitutive relation that allows for creep and the shortcoming that it does not allow for stress relaxation. The research and study of the limiting strain models has attracted the attention of many investigators. In the present paper, the author discusses the existence of the displacement after a careful review of local-in-time existence results. It is shown that the energy diminishes with time. The proves, in addition to other results, the existence of the global solutions utilizing the investigation about the energy and a lemma where the blow-up conditions are stated and proven. The paper is quite mathematical and derives the required results by employing a number of theorems and lemmas. For the entire collection see [Zbl 1495.74001].
generalized Kelvin-Voigt viscoelastic model
scientific article; zbMATH DE number 7598425
scientific article