A new shell formulation for graphene structures based on existing ab-initio data

Abstract

An existing hyperelastic membrane model for graphene calibrated from ab-initio data (Kumar and Parks, 2014) is adapted to curvilinear coordinates and extended to a rotation-free shell formulation based on isogeometric finite elements. Therefore, the membrane model is extended by a hyperelastic bending model that reflects the ab-inito data of Kudin et al. (2001). The proposed formulation can be implemented straight-forwardly into an existing finite element package, since it does not require the description of molecular interactions. It thus circumvents the use of interatomic potentials that tend to be less accurate than ab-initio data. The proposed shell formulation is verified and analyzed by a set of simple test cases. The results are in agreement to analytical solutions and satisfy the FE patch test. The performance of the shell formulation for graphene structures is illustrated by several numerical examples. The considered examples are indentation and peeling of graphene and torsion, bending and axial stretch of carbon nanotubes. Adhesive substrates are modeled by the Lennard-Jones potential and a coarse grained contact model. In principle, the proposed formulation can be extended to other 2D materials.

New examples are added and some typos are removed. The previous results are unchanged, International Journal of Solids and Structures (2017)

References in corpus (9)

• Atomic Structure of Graphene on SiO2
• A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
• Interfacial adhesion between graphene and silicon dioxide by density functional theory with van der Waals corrections
• The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers
• Curvature dependent surface energy for a free standing monolayer graphene: some closed form solutions of the nonlinear theory
• Curvature dependent surface energy for free standing monolayer graphene: geometrical and material linearization with closed form solutions
• The exponentiated Hencky-logarithmic strain energy. Improvement of planar polyconvexity
• Constitutive modeling of some 2D crystals: graphene, hexagonal BN, MoS${}_2$, WSe${}_2$ and NbSe${}_2$
• Adhesion mechanics of graphene on textured substrates

Cited by in corpus (9)

• The multiplicative deformation split for shells with application to growth, chemical swelling, thermoelasticity, viscoelasticity and elastoplasticity
• Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities
• A new efficient hyperelastic finite element model for graphene and its application to carbon nanotubes and nanocones
• Comparing quantum, molecular and continuum models for graphene at large deformations
• A continuum contact model for friction between graphene sheets that accounts for surface anisotropy and curvature
• An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split
• Atomistically-informed continuum modeling and isogeometric analysis of 2D materials over holey substrates
• An Atomistic-based Finite Deformation Continuum Membrane Model for Monolayer Transition Metal Dichalcogenides
• A nonlinear hyperelasticity model for single layer blue phosphorus based on ab-initio calculations