Viscoelasticity with limiting strain

Yasemin Şengül

doi:10.3934/dcdss.2020330

Article Contents

2021, Volume 14, Issue 1: 57-70. Doi: 10.3934/dcdss.2020330

This issue Previous Article Cahn-Hilliard equation with capillarity in actual deforming configurations Next Article Adaptive time stepping in elastoplasticity

Viscoelasticity with limiting strain

Yasemin Şengül

Faculty of Engineering and Natural Sciences, Sabanci University, Tuzla 34956, Istanbul, Turkey

Dedicated to Alexander Mielke on the occasion of his 60th birthday

Received: May 31, 2019

Revised: September 30, 2019

Early access: April 2020

Published: January 2021

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Abstract

A self-contained review is given for the development and current state of implicit constitutive modelling of viscoelastic response of materials in the context of strain-limiting theory.

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Mathematics Subject Classification: Primary: 74D99, 74A20, 35Q74; Secondary: 74A05, 74A10.

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Figure 1. Limiting strain behaviour

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Figure 2. Experimental data for the stress-strain relationship for porcine carotid and thoracic artery tissues (cf. [43])

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Figure 3. Left. Model A: $ g(T) = \beta T + \alpha \left(1 + \frac{\gamma}{2} T^{2}\right)^{n} T $; Model B: $ g(T) = \frac{T}{(1 + |T|^{r})^{1/r}} $; Model C: $ g(T) = \alpha \left\{\left[1 - \exp\left(- \frac{\beta T}{1 + \delta |T|}\right)\right] + \frac{\gamma T}{1 + |T|} \right\} $; Model D: $ g(T) = \alpha \left(1-\frac{1}{1 +\frac{ T}{1 + \delta |T|}}\right) + \beta \left(1 + \frac{1}{1 + \gamma T^{2}}\right)^{n} T $, where $ \alpha, \beta, \gamma, \delta, n $ and $ r > 0 $ are constants. Right. General linear, quadratic and cubic nonlinearities

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