# American Institute of Mathematical Sciences

January  2021, 14(1): 57-70. doi: 10.3934/dcdss.2020330

## Viscoelasticity with limiting strain

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

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

Received  June 2019 Revised  October 2019 Published  January 2021 Early access  April 2020

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.

Citation: Yasemin Şengül. Viscoelasticity with limiting strain. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 57-70. doi: 10.3934/dcdss.2020330
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##### References:
Limiting strain behaviour
Experimental data for the stress-strain relationship for porcine carotid and thoracic artery tissues (cf. [43])
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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