Finite element methods for the non‐linear mechanics of crystalline sheets and nanotubes

By Marino Arroyo, Ted Belytschko. 2004

162 citations recorded by the source corpus.

The formulation and finite element implementation of a finite deformation continuum theory for the mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved monolayer lattices by means of the exponential Cauchy–Born rule. The constitutive model for a two‐dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the underlying atomistic model. The resulting hyper‐elastic potential depends on the stretch and the curvature of the surface, as well as on internal elastic variables describing the rearrangements of the crystal within the unit cell. Coarse grained calculations of carbon nanotubes (CNTs) are performed by discretizing this continuum mechanics theory by finite elements. A smooth discrete representation of the surface is required, and subdivision finite elements, proposed for thin‐shell analysis, are used. A detailed set of numerical experiments, in which the continuum/finite element solutions are compared to the corresponding full atomistic calculations of CNTs, involving very large deformations and geometric instabilities, demonstrates the accuracy of the proposed approach. Simulations for large multi‐million systems illustrate the computational savings which can be achieved. Copyright © 2003 John Wiley & Sons, Ltd.

Subfields: Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/673e15924c5371ba5bdef2dbbf2f7b07580eb097

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In Materials Chemistry

Citations in the corpus

Reinforcing efficiency of nanoparticles: A simple comparison for polymer nanocomposites (2008, background): “, the complex buckling pattern of multiwalled carbon nanotubes, to be studied [8].”
NONLINEAR MECHANICS OF SINGLE-ATOMIC-LAYER GRAPHENE SHEETS (2009, methodology): “For the 2nd generation Brenner potential, the bending modulus was found to be 1.8 eV Å2/atom or equivalently, 0.11 nNnm [Arroyo and Belytschko, 2004a].”
A bridging domain and strain computation method for coupled atomistic–continuum modelling of solids (2007, methodology): “The angle-bending term is of the following form: Eangle = (1)2k ( − 0)(2)[1 + ksextile( − 0)(4)] (78) Young’s modulus and the Poisson’s ratio can be then obtained through the Cauchy–Born rule [21].”
On the L2 and the H1 couplings for an overlapping domain decomposition method using Lagrange multipliers (2007, methodology): “[24] to couple the Arroyo and Belytschko [25] shell formulation to molecular mechanics.”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, unknown): “The indirect couplings are usually taken from the corresponding isotropic spectra of the solute or from the literature, and kept fixed.”
Shape control of active surfaces inspired by the movement of euglenids (2014, background): “More details are given in Arroyo and Belytschko (2004).”
Characterizing and Modeling Mechanical Properties of Nanocomposites-Review and Evaluation (2010, background): “Although the applicability of continuum mechanics (including micro mechanics) to nanocomposites has been subjected to debate [59,63], many recent works directly applying continuum mechanics to nanostructures and nanomaterials have reported meaningful results and elucidated many issues [64-73].”