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A.Y. Matveeva, H. J. Böhm, F.W.J. van Hattum:
"Seminanalytical Stiffness Tensor Approximation for Polymers Reinforced with Curved Nanotubes";
in: "Proceedings of Composites Week at Leuven 2013 and TexComp-11 Conference", A.W. van Vuure (Hrg.); Katholieke Universiteit Leuven, Leuven, 2013, 8 S.

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.