Band 23, Heft 5-6

This paper elaborates that at micro/nanoscales, highly curved matter spaces may induce abnormal driving forces. Such abnormal driving forces are controlled by two fundamental factors: one is the bending extent of surfaces (curvature) and another is the non-uniform extent of bending surfaces (the gradients of curvatures).

The fields of nanotechnology and nanoscience are full of opportunities and challenges. The needed modification of classical continuum mechanics to account for the dramatically novel characteristics and phenomena determining the mechanical response of nanomaterials/structures remains an ambitious goal pursued by mechanics researchers. The theory of surface elasticity proposed by Gurtin and Murdoch has been shown to be an important tool in theoretical nanomechanics. In this paper, we present an overview of recent advances in application of surface elasticity theory at the nanoscale. In particular, we focus on the elastic and plastic deformation, vibration and buckling, fracture and contact behavior of nanoscale solids from one dimension to three dimensions. We hope that this contribution can provide a valuable insight into nanomechanics analysis methods by taking surface effects into account. The results may help to bridge the gap between conventional mechanics and findings from simulation and experiment, in such areas as multifunctional material and micro-electro-mechanical systems.

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen’s nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

Equilibrium equations and boundary conditions of the strain gradient theory in arbitrary curvilinear coordinates have been obtained. Their special form for an axisymmetric plane strain problem is also given.

A filtration model for plastic flow based on the idea of a deformed material considered as a two-phase heterogeneous medium has been suggested. In this approach, the wave displacement is regarded as a shock transition in the medium. One of the phases (the excited one) is responsible for system restructuring, and the other phase (the normal one) is unrelated to structural transformations. The plastic wave is the result of the interaction of these two phases. The governing equations for the filtration model are obtained. They include the laws of momentum and mass conservation, as well as the filtration ratio of the phases.

Generalized continuum theories for materials and processes have been introduced in order to account in a phenomenological manner for microstructural effects. Their drawback mainly rests in the determination of the extra phenomenological coefficients through experiments and simulations. It is shown here that a graphical representation of the local topology describing deformation models can be used to deduce restrictions on the phenomenological coefficients of the gradient elasticity continuum theories.

The present paper deals with the study of reflection waves in an initially stressed transversely isotropic medium, in the context of Green and Naghdi (GN) thermoelasticity theory type II and III. The components of displacement, stresses and temperature distributions are determined through the solution of the wave equation by imposing the appropriate boundary conditions. Numerically simulated results are plotted graphically with respect to frequency in order to show the effect of anisotropy.