Melanie Todt

Thermal expansion of rock-salt cubic AlN

We combine continuum mechanics modeling and wafer curvature experiments to characterize the thermal expansion coefficient of AlN in its metastable cubic rock-salt (B1) structure. The latter was stabilized as nm thin layers by coherency strains in CrN/AlN epitaxial multilayers deposited on Si (100) substrates using reactive magnetron sputtering. The extraction of the B1-AlN thermal expansion coefficient, from experimentally recorded temperature dependent wafer curvature data, is formulated as an inverse problem using continuum mechanics modeling. The results are cross-validated by density functional theory calculations.

Elastic properties of graphene obtained by computational mechanical tests

The basic building block of many carbon nanostructures like fullerenes, carbon onions or nanotubes is the truly two-dimensional material graphene. Commercial finite element codes, widely used to predict the mechanical properties of these structures, rely on the knowledge of the mechanical properties of the basic material. In this paper using an atomistic simulation approach we determine the membrane and bending stiffness of graphene, as well as the corresponding effective parameters: the effective elastic modulus , Poisson ratio and thickness . It is shown that within reasonable accuracy the obtained parameters can be applied to various loading scenarios on carbon nanostructures as long as the characteristic length of these structures is larger than . Thus, for such large and complex structures that withstand an analytical or atomistic description, commercial finite element solvers, in combination with the found effective parameters, can be used to describe these structures.

Shell-Models for Multi-Layer Carbon Nano-Particles

In many cases continuum mechanics has proved to be an appropriate method for investigating the mechanical behavior of carbon nanostructures reducing the computational requirements compared to atomistic methods significantly. The main modeling issues arising in continuum mechanics modeling of multi-layer carbon nanostructures are briefly discussed. These issues involve the continuum modeling of (i) the atomic layers, (ii) the covalent interlayer bonds, (iii) the van der Waals interactions, and (iv) the excess surface energy due to curvature. Continuum mechanics methods in conjunction with the finite element method are applied to investigate the compressive behavior of carbon crystallites and a possible growth limit of carbon onions.

A multiscale approach for modelling impact on woven composites under consideration of the fabric topology

A computationally efficient multiscale modelling approach for predicting impact damage within fabric reinforced laminated composites is presented. In contrast to common ply-level approaches, the topology of a multi-layered fabric reinforced laminate is resolved at tow-level for a sub-domain embedded in a shell layer with homogenised representation of the laminate. The detailed sub-domain is entirely modelled using shell elements, where material nonlinearities such as damage and plasticity-like behaviour of the tows, inelastic behaviour of unreinforced resin zones up to failure and delamination between plies are accounted for. To exemplify the capabilities of the approach, an explicit finite element simulation of a laminated plate consisting of eight carbon fabric reinforced epoxy plies with eight harness satin weaving style in a drop weight impact test setup is conducted. The spatial and temporal distribution of intra- and inter-ply damage is predicted and the total energy absorption by the plate, as well as the contributions of individual damage mechanisms are evaluated. The predictions show very good agreement with corresponding experimental data from the literature and give insight into the impact behaviour of the laminate beyond the capability of usual experiments. The new approach allows to resolve the stress concentrations due to fabric topology in detail. Compared to common ply-level approaches this is reflected in different predicted energy absorptions per mechanism although, the total energy absorption hardly differs. This is especially important when the post impact behaviour of laminates is predicted as it is strongly influenced by the extent of the individual damage mechanisms.

Atomistic and continuum modelling of graphene and graphene-derived carbon nanostructures

Nanometer sized particles formed by carbon atoms mainly arranged in a hexagonal atomic structure are called carbon nanostructures (CNS). In this chapter we focus exclusively on sp 2-bonded CNS that include graphene (Geim, 2009; Geim and Novoselov, 2007), single- and multi-walled carbon nanotubes (Iijima, 1991; Pantano et al., 2004), fullerenes (Kroto et al., 1985), and carbon onions (Banhart and Ajayan, 1996; Kroto, 1992; Ugarte, 1992, 1995). Especially graphene has drawn a lot of attention within the last years, because it possesses exceptional mechanical and electrical properties (Geim, 2009; Novoselov et al., 2004) and a high thermal conductivity (Lau et al., 2012). It is the main building block of all other CNS based on sp 2-bonded carbon, which therefore should inherit its exceptional properties making them promising candidates for applications in the field of structural mechanics and the electronics industry, as fillers in nanocomposites (Choi and Lee, 2012; Baughman et al., 2002; Stankovich et al., 2006) and as solid lubricants (Hirata et al., 2004). This chapter will focus on the amazing mechanical properties of CNS only. Information regarding the extraordinary electronic and thermal properties can be found elsewhere (Novoselov et al., 2004; Castro Neto et al., 2009; Balandin, 2011).