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Content available remote Self-consistent approach of the constitutive law of a two-phase visco-elastic material described by fractional derivative models
Dinzart F., Lipiński P.
Archives of Mechanics
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2010
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Vol. 62, nr 2
135-156
EN
The constitutive law of a two-phase isotropic polymer blending described by fractional derivative models is obtained through a classical self-consistent scheme. A parametric analysis is driven to describe the influence of the four parameters associated with the constitutive law description and to comprise the conditions of application of the model. An identification of the set of parameters is performed by mechanical spectroscopy for two amorphous polymers: the polymethyl methacrylate (PMMA) and the styrene acrylonytrile copolymer (SAN) and their mixture, to evaluate the ability of the model to reproduce the experimental results obtained from the Dynamic Mechanical Thermal Analysis.
2
Content available remote Improved five-parameter fractional derivative model for elastomers
Dinzart F., Lipiński P.
Archives of Mechanics
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2009
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Vol. 61, nr 6
459-474
EN
The dynamic behaviour of elastomers is assumed to follow a constitutive differential equation of non-integral (fractional) order. In order to describe the peculiar frequency response of the loss factor, the constitutive equation has been refined by introducing the fifth parameter to the classical fourth-order equation. The asymmetry of the loss factor in the frequency domain comes from the different time-derivative orders of the stress and strain. Either smooth asymmetry or stabilization by a plateau at high frequency can be modelled by suitable difference between the two orders of the time derivatives. The physical validity of the model is discussed and a parametrical analysis is conducted on diagrams relating the height and the width of the loss factor.
3
Content available remote Thermomechanical response of a viscoelastic beam under cyclic bending; self-heating and thermal failure
Dinzart F., Molinari A., Herbach R.
Archives of Mechanics
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2008
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Vol. 60, nr 1
59-85
EN
The thermomechanical response of beams made up of thermoplastic polymer is analysed in the case of cyclic bending. The material behavior is modelled by a viscoelastic law depending on temperature and frequency. Inertia effects are neglected. The stress, strain and temperature distributions are expressed as functions of the beam geometry, the loading parameters and the material characteristics. The stability of the steady-state solutions is analysed with use of a linear perturbation approach. The conditions for thermal runaway (thermo-mechanical instability) are explored.
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