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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Figure 2. Experimental data for the stress-strain relationship for porcine carotid and thoracic artery tissues (cf. [43])
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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Limiting strain behaviour
Experimental data for the stress-strain relationship for porcine carotid and thoracic artery tissues (cf. [43])
Left. Model A: