An atomistic-based finite deformation continuum membrane model for monolayer Transition Metal Dichalcogenides
Document Type
Article
Publication Date
11-2022
Department
Department of Mechanical Engineering-Engineering Mechanics
Abstract
A finite-deformation crystal-elasticity membrane model for Transition Metal Dichalcogenide (TMD) monolayers is presented. Monolayer TMDs are multi-atom-thick two-dimensional (2D) crystalline membranes having atoms arranged on three parallel surfaces. In the present formulation, the deformed configuration of a TMD-membrane is represented through the deformation map of its middle surface and two stretches normal to the middle surface. Crystal-elasticity-based kinematic rules are employed to express the deformed bond lengths and bond angles of TMDs in terms of the continuum strains. The continuum hyper-elastic strain energy of the TMD membrane is formulated from its inter-atomic potential. The relative shifts between two simple lattices of TMDs are also considered in the constitutive relation. A smooth finite element framework using B-splines is developed to numerically implement the present continuum membrane model. The proposed model generalizes the crystal-elasticity-based membrane theory of purely 2D membranes, such as graphene, to the multi-atom-thick TMD crystalline membranes. The significance of relative shifts and two normal stretches are demonstrated through numerical results. The proposed atomistic-based continuum model accurately matches the material moduli, complex post-buckling deformations, and the equilibrium energies predicted by the purely atomistic simulations. It also accurately reproduces the experimental results for large-area TMD samples containing tens of millions of atoms.
Publication Title
Journal of the Mechanics and Physics of Solids
Recommended Citation
Yadav, U.,
&
Ghosh, S.
(2022).
An atomistic-based finite deformation continuum membrane model for monolayer Transition Metal Dichalcogenides.
Journal of the Mechanics and Physics of Solids,
168.
http://doi.org/10.1016/j.jmps.2022.105033
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/16377