Author
Erbay, Hüsnü Ata, Erkip, A., Şengül, Y.
Publication Date
2020-11-15
Publication Place
-
Elsevier
Subject
Viscoelasticity, Strain-limiting theory, Initial-value problem, Local existence
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
0022-0396
Record ID
fe238ab2-62d6-49e8-a560-b742ff67e26b
Library Location
Natural and Mathematical Sciences
Date
2020-11-15
Notes
TÜBİTAK
Sample Text
In this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of the linearized strain and the stress. The model is a generalization of the nonlinear Kelvin-Voigt viscoelastic solid under the assumption that the strain and the strain rate are small. We define an initial-value problem for the stress variable and then, under the assumption that the nonlinear constitutive function is strictly increasing, we convert the problem to a new form for the sum of the strain and the strain rate. Using the theory of variable coefficient heat equation together with a fixed point argument we prove local existence of solutions. Finally, for several constitutive functions widely used in the literature we show that the assumption on which the proof of existence is based is not violated.
DOI
10.1016/j.jde.2020.06.052
Cilt
269
