Continuum mechanics

About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.

Terahertz wave propagation in uniform nanorods: A nonlocal continuum mechanics formulation including the effect of lateral inertia

Abstract: The dynamic testing of materials and components often involves predicting the propagation of stress waves in slender rods. The present work deals with the analysis of the wave propagation characteristics of nanorods. The nonlocal elasticity theory and also the lateral inertia are incorporated into classical/local rod model to capture unique features of the nanorods under the umbrella of continuum mechanics theory. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behaviors of nanorods from those of macroscopic rods. Nonlocal rod/bar model is developed for nanorods including the lateral inertia effects. The analysis shows that the wave characteristics are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The wave propagation properties of the nanorod obtained from the present formulations are compared with the continuum rod model, nonlocal second and fourth order strain gradient models, Born-K a ´ rm a ´ n model and the nonlocal stress gradient model. It has also been shown that, the unstable second order strain gradient model can be replaced by considering the inertia gradient terms in the formulations. The effects of both the nonlocal scale and the diameter of the nanorod on spectrum curves are highlighted in the present manuscript. The results provided in this article are useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Discontinuous deformation gradients near the tip of a crack in finite anti-plane shear: an example

Abstract: This investigation aims at the elastostatic field near the edges (tips) of a plane crack of finite width in an all-round infinite body, which — at infinity — is subjected to a state of simple shear parallel to the crack edges. The analysis is carried out within the fully nonlinear equilibrium theory of homogeneous and isotropic, incompressible elastic solids. Further, the particular constitutive law employed here gives rise to a loss of ellipticity of the governing displacement equation of equilibrium in the presence of sufficiently severe anti-plane shear deformations.

Micro-mechanics of crack initiation

Abstract: Prior to the crack initiation, damage is most often localized at a scale below the size of the classical representative volume element of the continuum mechanics. This allows the stress and strain analyses in a component to neglect the strain-damage coupling at macro-scale. At the micro-scale, this coupling plays a very important role which can be emphasized by a two scale element of an elastoplastic damaged micro-element embedded in an elastic or elastoplastic macro-element. The Lin-Taylor hypothesis of strain compatibility allows the determination of the damage at micro-scale by solving the coupled constitutive equations for a given macro-strain history. It is shown how this model may be cast in the form of a post-processor of a finite element code and how a simple damage law coupled with strain constitutive equations replicates the main features of ductile or creep crack initiation, low cycle and high cycle fatigue for the case of a three-dimensional state of stress.