*Proceedings of Composites Week at Leuven 2013 and TexComp-11 Conference*,

Katholieke Universiteit Leuven, 2013

### SEMIANALYTICAL STIFFNESS TENSOR APPROXIMATION FOR POLYMERS
REINFORCED WITH CURVED NANOTUBES

A. Mateeva^{1}, H.J. Böhm^{2},
F.H.W. van Houtten^{1}

^{1}Institute for Polymers and Composites,

University of Minho, Guimarães, Portugal

^{2}Institute of Lightweight Design and Structural
Biomechanics,

TU Wien,
Vienna, Austria

**Abstract** -
Two approaches based on continuum mechanics have been proposed to determine the
effective elastic moduli of polymers reinforced with curved carbon nanotubes.
Curliness is represented by distributions of nanotubes in cube-shaped volume
elements by using sequences of segments joined together at randomly chosen
angles using Monte Carlo simulation.
In the first method carbon nanotubes are embedded into the matrix as beam
finite elements with different concentrations from 0.5 up to 7% by weight
fraction.
Six load cases are applied to RVEs with periodic boundary conditions for
extracting the full stiffness tensor.
The second approach combines the finite element method and analytical
micromechanical models.
Nanotubes are distributed in a cube with concentrations of 0.1% by volume
fraction.
Waviness parameters are chosen the same as in the first method.
By applying 6 load cases and specific mixed boundary conditions dilute stress
concentration tensors are calculated and incorporated into analytical Mori
Tanaka models to calculate the full stiffness tensors for composites with
different concentrations.
Results are compared with experimental data for injection moulded samples:
polycarbonate reinforced with MWCNT.

(hjb,131009)