Section 6: Material modelling in solid mechanics - GAMM 2012

24 Section 6: Material modelling in solid mechanics
individual materials constituents. It was found that for the considered composites have place the
additional peak damping properties, which is realized for very small thicknesses of the viscoelastic
phase. This peak is still about a factor 20 or so compared to the loss modulus of the pure matrix.
We demonstrated that by introducing thin layers of a viscoelastic material, one can significantly
increase the loss characteristics of discrete morphology multiphase materials. The layered fibers
composites are also considered. It is shown that for such materials may be implemented at the
same time as high elastic properties, and abnormally high damping properties.
[1] A.A.Gusev , S.A. Lurie, Loss amplification effect in multiphase materials with viscoelastic
interfaces. Macromolecules (2009) 42,14, 5372 – 5377.
Modeling of composite structural elements made from aramid fiber using the method
of features objects
Michał Majzner, Andrzej Baier (Silesian University of Technology)
The use of modern materials such as composite materials, enabling the production of new or modifying
existing design solutions, improve their technical characteristics, while use in the process
of design and engineering and manufacturing, will allow the modification of endurance, physical
and chemical properties to match the features and functionality that are comply with. In research
studies, it is proposed to systematize and formalize elementary objects in the context of modeling
and fabrication of objects created on the basis of structural fiber composites. Application of features
objects methods was shows on an example of modeling the structural element, in the form
of an existing manufactured from steel, which was modified and converted with aramid fiber. It
was necessary to carry out research in the form of numerical analysis, examining the strength of
the modified object.
On the fibres shape effect for non-linear and unidirectional stationary heat conduction
in two-phase hollow cylinder with radially graded material properties
Piotr Ostrowski (Technical University of Lodz)
The main aim of this paper is to consider unidirectional and stationary heat conduction in the
infnite two-phase hollow cylinder with temperature dependent material properties. The deterministic
microstructure of this composite is periodic (for a fixed radius) along the angular axis
and has slowly varying effective properties in the radial direction. Therefore, we deal here with
a special case of functionally graded materials, FGM, c.f. Suresh, Mortensen (1998). One of the
components is called fibre, which is arranged in considered hollow cylinder with circular pattern.
The physical phenomenon of the heat transfer is described by well known Fourier’s equation
c ˙ θ − ∇(K∇θ) = 0, (1)
which contains temperature dependent (in this case), highly oscillating and discontinuous coefficients
of K = K(θ) - heat conduction tensor, and c = c(θ) - specific heat. To this macroscopic
model the tolerance averaging approximation will be used, cf. Wozniak, Wierzbicki (2000). The
general approach to the description of longitudinally graded stratified media can be found in
[Wozniak, Michalak, Jedrysiak 2008]. The fibres width function g = g(r) of radius r will be examined
and its effects on the temperature field. The averaged differential equation has smooth
and slowly varying coefficients, hence in some special cases, for boundary value problem, analytical
solution can be obtained. In other cases, numerical methods have to be used. This model
takes into account the effect of microstructure size on the overall heat transfer behaviour.