Nonlocal Euler-Bernoulli Beam Theories With Material Nonlinearity and Their Application to Single-walled Carbon Nanotubes

The small-scale effect and the material nonlinearity significantly impact the mechanical properties of nanobeams. However, the combined effects of two factors have not attracted the attention of researchers. In the present paper, we proposed two new nonlocal theories to model mechanical properties of slender nanobeams for centroid locus stretching or inextensional effect respectively. Two new theories consider both the material nonlinearity and the small-scale effect induced by the nonlocal effect. The new models are used to analyze the static bending and the forced vibration for single-walled carbon nanotubes (SWCNTs). The results indicate that the stiffness softening effect induced by the material nonlinearity has more prominent impact than the nonlocal effect on SWCNT’s mechanical properties. Therefore, neglecting the material nonlinearity may cause qualitative mistakes.

Nonlocal Euler-Bernoulli Beam Theories with Material Nonlinearity and their Application to Single-Walled Carbon Nanotubes

The small-scale effect and the material nonlinearity significantly impact the mechanical properties of nanobeams. However, the combined effects of two factors have not attracted the attention of researchers. In the present paper, under the displacement’s Euler-Bernoulli assumption, we proposed two new nonlocal models to describe the mechanical properties of slender nanobeams for two centroid locus conditions: the locus extensibility and the locus inextensibility. Two new theories consider both the material nonlinearity and the small-scale effect induced by the non-local effect. The new models are used to analyze the static bending and the forced vibration for single-walled carbon nanotubes (SWCNTs). The results indicate that the stiffness’ softening effect induced by the material nonlinearity has more prominent impact than the nonlocal effect on SWCNT’s mechanical properties. Therefore, neglecting the material nonlinearity may cause qualitative mistakes.

Surface Roughness Effects on Self-Interacting and Mutually Interacting Rayleigh Waves

Rayleigh waves are very useful for ultrasonic nondestructive evaluation of structural and mechanical components. Nonlinear Rayleigh waves have unique sensitivity to the early stages of material degradation because material nonlinearity causes distortion of the waveforms. The self-interaction of a sinusoidal waveform causes second harmonic generation, while the mutual interaction of waves creates disturbances at the sum and difference frequencies that can potentially be detected with minimal interaction with the nonlinearities in the sensing system. While the effect of surface roughness on attenuation and dispersion is well documented, its effects on the nonlinear aspects of Rayleigh wave propagation have not been investigated. Therefore, Rayleigh waves are sent along aluminum surfaces having small, but different, surface roughness values. The relative nonlinearity parameter increased significantly with surface roughness (average asperity heights 0.027–3.992 μm and Rayleigh wavelengths 0.29–1.9 mm). The relative nonlinearity parameter should be decreased by the presence of attenuation, but here it actually increased with roughness (which increases the attenuation). Thus, an attenuation-based correction was unsuccessful. Since the distortion from material nonlinearity and surface roughness occur over the same surface, it is necessary to make material nonlinearity measurements over surfaces having the same roughness or in the future develop a quantitative understanding of the roughness effect on wave distortion.

Topology Optimization using the Discrete Element Method. Part 2: Material Nonlinearity

Structural Topology Optimization typically features continuum-based descriptions of the investigated systems.In Part 1 we have proposed a Topology Optimization method for discrete systems and tested it on quasi-static 2D problems of energy minimization, assuming linear elastic material.However, discrete descriptions become particularly convenient in the failure and post-failure regimes, where discontinuous processes take place, such as fracture, fragmentation, and collapse. Here we take a first step towards failure problems, testing Discrete Element Topology Optimization for systems with nonlinear material responses. The incorporation of material nonlinearity does not require any change to the optimisation method, only using appropriately rich interaction potentials between the discrete elements. Three simple problems are analysed, to show how various combinations of material nonlinearity in tension and compression can impact the optimum geometries. We also quantify the strength loss when a structure is optimized assuming a certain material behavior, but then the material behaves differently in the actual structure. For the systems considered here, assuming weakest material during optimization produces the most robust structures against incorrect assumptions on material behavior. Such incorrect assumptions, instead, are shown to have minor impact on the serviceability of the optimized structures.