We have studied the mechanical properties of suspended graphene membranes using molecular dynamics (MD) and generalized continuum elasticity theory (GE) in order to develop and assess a continuum description for graphene. The MD simulations are based on a valence force field model which is used to determine the deformation and the elastic energy of the membrane (E MD ) as a function of external forces. For the continuum description, we use the expression E cont = E stretching + E bending for the elastic energy functional. The elastic parameters (tensile rigidity and Poisson ratio) entering E cont are determined by requiring that E cont = E MD for a set of deformations.Comparisons with the MD results show excellent agreement. We find that the elastic energy of a supported graphene sheets is typically dominated by the nonlinear stretching terms whereas a linear description is valid only for very small deflections. This implies that in some applications, i.e. NEMS, a linear description is of limited applicability.
Auxetic materials with negative Poisson’s ratio have\ud
recently attracted the interest of the scientific community. This\ud
is because these materials have the potential to deliver specific\ud
functions thanks to a discretization of their constitutive matter\ud
that is intended as an aggregation of macro-scaled cellular\ud
structures characterized by specific geometries. Many auxetic\ud
structures with different geometries and auxetic response have\ud
been proposed. Downscaling the cellular structures (e.g. microscale)\ud
has the potential to improve the overall auxetic\ud
properties of the material, yet there is not enough research on\ud
the behavior of these structures at the microscale. This paper\ud
studies the auxetic behavior of a modified hexachiral structure\ud
formed by microscale elements. First an optimization study was\ud
performed to define the most appropriate geometrical\ud
dimensions. Then the auxeticity of the proposed cell was\ud
assessed carefully introducing a new Coefficient of Auxeticity\ud
which allowed to capture complex mechanical responses (e.g.\ud
including cellular rotations) as those faced with the proposed\ud
design. The proposed miniaturized design shows an\ud
outstanding stable auxetic response up to 20% strain of the\ud
micro-cell. It is believed that this study has the potential to\ud
pave the way to a new class of auxetic materials
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