A modified core-shell (MC-S) model is proposed to investigate the effect of surface elasticity on the elastic properties of nanowires under bending and tension loading modes. The continuous exponential function based on bulk elasticity is applied to the surface region of nanowires to better describe the elasticity in the surface layer. Two parameters related to the surface, namely, the inhomogeneous degree constant α̃, and the transition region of this inhomogeneous state rs (i.e., surface layer thickness), are introduced for examining the size effects of the elastic modulus of the overall nanowires. A strong size dependence of elasticity is revealed under both bending and tension loads. Furthermore, the theoretical solution for an effective Young’s modulus with relevant experiments, as well as the results of a molecular statistical thermodynamics (MST) method for zinc oxide (ZnO) nanowires, and a molecular dynamics (MD) simulation for silicon (Si) nanowires, are compared. It is shown that the theoretical curves not only agree well with the experimental data, but also fit the computational results (MST or MD) approximately below 20 nm. As a result, our model can predict the behavior of surface elasticity, with respect to the lateral size of nanostructures at a relatively small scale, no matter how stiff or soft the surface of the nanomaterials.

A novel three-dimensional graphene-like networks material (3D-GLN) exhibiting the hierarchical porous structure was fabricated with a large-scale preparation method by employing an ion exchange resin as a carbon precursor. 3D-GLN was first studied as the effective microwave absorbing material. As indicated from the results of the electromagnetic parameter tests, and the minimum reflection loss (R_L) of the 3D-GLN reached −34.75 dB at the frequency of 11.7 GHz. To enhance the absorption performance of the nonmagnetic 3D-GLN, the magnetic Fe₃O₄ nanoparticles were loaded on the surface of the 3D-GLN by using the hydrothermal method to develop the 3D-GLN/Fe₃O₄ hybrid. The hybrid exhibited the prominent absorbing properties. Under the matching thickness of 3.0 mm, the minimum R_L value of hybrid reached −46.8 dB at 11.8 GHz. In addition, under the thickness range of 2.0–5.5 mm, the effective absorption bandwidth (R_L < 10 dB) was 13.0 GHz, which covered part of the C-band and the entire X-band, as well as the entire Ku-band. The significant microwave absorption could be attributed to the special 3D network structure exhibited by the hybrid and the synergistic effect exerted by the graphene and the Fe₃O₄ nanoparticles. As revealed from the results, the 3D-GLN/Fe₃O₄ hybrid could be a novel microwave absorber with promising applications.

The complex variable method for solving the two-dimensional thermal stress problem of octagonal quasicrystals is stated. The closed-form solutions for octagonal quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors and energy release rate are presented.

The size-dependent elastic property of rectangular nanobeams (nanowires or nanoplates) induced by the surface elasticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 100 nm. It is also found that the theoretical results calculated by a modified core-shell model have more obvious advantages than those by other models (core-shell model and core-surface model) by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers.