Article Contents
Article Contents

# Viscoelasticity with limiting strain

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

• 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.

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

 Citation:

• Figure 1.  Limiting strain behaviour

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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