2011 **Abstract:**

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This paper describes a nonlinear rheological model consisting of a modified and extended classical Voigt model for predicting the time dependent deformation of a variety of viscoelastic materials exhibiting elastic, viscous and inertial nonlinearities simultaneously. The usefulness of the model is illustrated by numerical examples.

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“…We can interpret each term present in Equation (9) following Monsia (2011f). The first term in Equation (9) is proportional to the basic inertial stress, the second to a nonlinear quadratic viscous stress, the third term to the linear viscous stress, the fourth term to the classical linear elastic stress and the last term to a quadratic nonlinear elastic stress.…”

confidence: 99%

“…We can interpret each term present in Equation (9) following Monsia (2011f). The first term in Equation (9) is proportional to the basic inertial stress, the second to a nonlinear quadratic viscous stress, the third term to the linear viscous stress, the fourth term to the classical linear elastic stress and the last term to a quadratic nonlinear elastic stress.…”

confidence: 99%

“…Note that in this present one-dimensional model, the stresses and strain are scalar functions and the coefficients a, b and c are time independent material parameters. Thus, noting t the total stress due to the external exciting force acting on the material, the superposition of elastic stress, viscous stress and inertial stress is given by (Monsia 2011f…”

confidence: 99%

“…The viscous and inertial stresses are derived as first and second time derivatives of a similar function to the pure elastic stress. Therefore, the superposition of these three stress components, for a nonlinear elastic spring force function ) ( of deformation , which is a scalar function, leads to the fundamental equation (Monsia, 2011g;Monsia, 2012) …”

confidence: 99%

“…Recently again, Monsia (2011f) using again the Bauer's approach (1984), proposed a nonlinear rheological model based on a substitution of linear elastic and damping forces in Voigt model by nonlinear elastic and damping forces with inclusion of a body for providing a theoretical basis to empirical exponential or logistic formulas used by several authors for fitting the stress-strain experimental data of arteries. Very lately, Monsia (2011g) by application of the Bauer's theory (1984), developed successfully for a variety of materials a nonlinear rheological model that can be used to predict and describe their dynamical behavior. By using a hyperbolic law as elastic spring force function (Monsia, 2011g), the strain versus time variation has been described as a hyper-exponential type function that appeared useful to reproduce the typical nonlinear exponential deformation of some viscoelastic materials.…”

confidence: 99%