Section 6: Material modelling in solid mechanics - GAMM 2012

16 Section 6: Material modelling in solid mechanics
asphalt cover layer, i.e. the top layer of the entire asphalt-construction. In order to predict the
macro-scale effective material properties of asphalt we apply a numerical homogenisation scheme
based on volume averaging techniques. The main advandtage of this numerical approach is, that
the effective material properties can be determined in knowledge of the micro-scale properties.
Hence, the first step towards an overall model for bituminous asphalt is the quantification of
the micro-scale mechanical properties. Against the background of solid-borne acoustical properties
we restrict ourselves to a geometrically linear description involving only small deformations
on both, macro- and micro-scale. Doing so, the linear-elastic properties of the stiff, granular filler
can be adopted from relevant literature. The viscoelastic behaviour of the bituminous phase is
characterized by rheological experiments (dynamic shear rheometer with plate-plate geometry).
The numerical implementation on the micro-scale is realized using a generalized Zener model (3d).
Making use of the numerical homogenization approach, the effective viscoelastic properties on
the macro-scale are investigated within transient experiments (relaxation/creep test). In particular
we are interested in the particular relaxation mechanisms and the related characteristic frequencies
to be observed on the macro-scale. The influence of micro-scale boundary conditions will be
taken into account. In order to study the interaction between micro-constituents as well as their
geometrical morphology on the one hand and the effective viscoelastic properties on the other,
we introduce artificially produced periodic unit cells based on simplified geometries with varying
volume and surface fractions of the mineral filler.
Jumps of the critical tracking loadings for viscoelastic beams with vanisihing internal
viscosity
S.A.Agafonov (Moscow State Technical University), D.V.Georgievskii (Moscow State University)
Transverse vibrations of a viscoelastic beam under action of a tracking loading are considered.
The constitutive relation represents the following non-linear connection of stress σ(t), strain ε(t)
and strain rate ˙ε(t):
σ = Eε +
where E is the Young modulus, k (n)
i
N
n
n=1 i=1
k (n)
i ε2(n−i) ˙ε 2i−1 , N ≥ 1
> 0 are the coefficients of internal viscosity.
Analytical and numerical investigation of dynamic stability in case N = 3, k (1)
1 = 0, k (2)
1 = 0,
k (1)
2 = 0 shows that if k (3)
α → 0 (k (3)
β
= 0, k(3)
γ = 0; (α, β, γ) may be some permutation of (1, 2, 3))
then three critical values of tracking loading corresponding to each nonzero coefficient of viscosity
k (3)
α less than the value for elastic system by a finite quantity.
Numerical modeling of a non-linear viscous flow in order to determine how parameters
in constitutive relations influence the entropy production
Wolfgang H. Müller, B. Emek Abali (TU Berlin)
Some rheological materials like melting polymers, cosmetic creams, ketchup, toothpaste can be
modeled as non-Newtonian fluids by using a non-linear constitutive relation. Flow of this kind
of amorphous matter can be considered as a thermodynamic process, and a solution of pressure,
velocity and temperature fields describe it fully. Since flow processes are generally irreversible,
entropy is produced leading to dissipation in the system. This energy loss can be measured
indirectly in a cone/plate viscometer which is used to determine viscosity of a Bingham fluid.
While dissipation is a measurable quantity we want to be able to calculate it. Thus the goal of
this work is to explain how to calculate entropy production using balance equations in a spatial