  For thin networked materials, which are spatial discrete structures
constructed by continuum components, a paradox on the effective thickness
defined by the in-plane and out-of-plane stiffnesses is found, i.e. the
effective thickness is not a constant but varies with loading modes. To reveal
the mechanism underneath the paradox, we have established a micromechanical
framework to investigate the deformation mechanism and predict the stiffness
matrix of the networked materials. It is revealed that the networked materials
can carry in-plane loads by axial stretching/compression of the components in
the networks and resist out-of-plane loading by bending and torsion of the
components. The bending deformation of components has a corresponding relation
to the axial stretching/compression through the effective thickness, as the
continuum plates do, while the torsion deformation has no relation to the axial
stretching/compression. The isolated torsion deformation breaks the classical
stiffness relation between the in-plane stiffness and the out-of-plane
stiffness, which can even be further distorted by the stiffness threshold
effect in randomly networked materials. Accordingly, a new formula is
summarized to describe the anomalous stiffness relation. This network model can
also apply in atomic scale 2D nanomaterials when combining with the molecular
structural mechanics model. This work gives an insight into the understanding
of the mechanical properties of discrete materials/structures ranging from
atomic scale to macro scale.
