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.

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.