Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Elastic Properties and Frequencies of Free Vibrations of Single-Layer Graphene Sheets

Abstract: We determine the basal plane stiffness and Poisson’s ratio of single layer graphene sheets (SLGSs) in armchair and zigzag directions by using molecular mechanics simulations of their uniaxial tensile deformations with the MM3 potential, and of their axial and bending vibrations. Both approaches give the basal plane stiffness equal to ∼340 N/m which agrees well with that reported in the literature and derived from results of indentation experiments on SLGSs and from the first principle calculations. The computed value of Poisson’s ratio equals 0.21 in both armchair and zigzag directions. Assuming that the response of a SLGS is the same as that of a plate made of a linear elastic, homogeneous, and isotropic material having Poisson’s ratio = 0.21, the in-plane stiffness of ∼340 N/m and the total mass equal to that of the SLGS, the thickness of the SLGS is found to be ∼1 A. Thus Young’s modulus and the shear modulus of a SLGS equal ∼3.4 TPa and ∼1.4 TPa, respectively. It is shown that mode shapes corresponding to the several lowest frequencies of the SLGS differ noticeably from those of an equivalent thin layer made of a linear elastic isotropic material with Young’s modulus = 3.4 TPa and the shear modulus = 1.4 TPa. Furthermore, a free– free SLGS vibrates about a plane bisecting its width rather than its thickness as predicted by the Euler Bernoulli beam theory. We also investigate the effect of pretension on the natural frequencies of SLGSs using MM simulations and correlate it to that of 1 A thick linear elastic plate found by analyzing its three-dimensional deformations. These results will help design SLGS nanomechanical resonators having frequencies in the THz range.

Microbuckle initiation in fibre composites : A finite element study

Abstract: A finite strain continuum theory is presented for unidirectional fibre reinforced composites under in-plane loading. The constitutive response is expressed in terms of couple stress theory, and is deduced from a unit cell of a linear elastic Timoshenko beam embedded in a non-linear elastic-plastic matrix. The continuum theory is implemented within a finite element framework and is used to analyse compressive failure of polymer matrix composites by fibre microbuckling. It is assumed that microbuckling initiates from an imperfection in the form of a finite elliptical region of fibre waviness. The calculations show that the compressive strength decreases with increasing imperfection spatial size from the elastic bifurcation value of Rosen (1965, Fibre Composite Materials, pp. 37–75, American Society Metals Seminar) to the imperfection-sensitive infinite band strength given by Fleck et al. [1995, J. Appl. Mech. 62, 329–337.].