2012 # A Theoretical Characterization of Time Dependent Materials by Using a Hyperlogistic-Type Model

**Abstract:** In this work, the classical mechanical Voigt model is modified and extended to finite deformations by using a rational elastic spring force function to describe accurately the nonlinear time-dependent deformation response of some viscoelastic materials. As theoretical results, a hyperlogistic-type function has been found as the deformation versus time relationship. This growth model appeared powerful to reproduce mathematically as shown by numerical works, any S-shaped experimental data. Compared with some pre…

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“…Very recently, the Bauer's rheological-dynamical theory was formulated in a simple mathematical expression that may be described by a single second order evolution equation within the framework of continuum mechanics for investigating the dynamics of viscoelastic material systems [12,13]. This formulation has successfully been applied in several papers to model creep deformation [13], creep relaxation [6] and deformation restoration process under stress relaxation conditions [14,15] of a variety of viscoelastic solid bodies.…”

confidence: 99%

“…Very recently, the Bauer's rheological-dynamical theory was formulated in a simple mathematical expression that may be described by a single second order evolution equation within the framework of continuum mechanics for investigating the dynamics of viscoelastic material systems [12,13]. This formulation has successfully been applied in several papers to model creep deformation [13], creep relaxation [6] and deformation restoration process under stress relaxation conditions [14,15] of a variety of viscoelastic solid bodies.…”

confidence: 99%

“…Therefore, an infinite number of functions φ may be designed. In doing so, various types of mathematical expressions for the function φ have been proposed in recent papers [6,[12][13][14][15]22]. In general, as performed by Bauer [7], the stiffness nonlinearity function φ(u) may be expanded in a power series as: ... ... ) (…”

confidence: 99%