Open Access

ARTICLE

A Lattice Statics-Based Tangent-Stiffness Finite Element Method

Peter W. Chung¹, Raju R. Namburu², Brian J. Henz³

1 Corresponding author, Computational and Information Sciences, Directorate, U.S. Army Research Laboratory, Aberdeen Proving, Ground, MD 21005-5067, pchung@arl.army.mil
2 U.S. ARL, CISD, APG, MD
3 U.S. ARL, CISD, APG, MD

Computer Modeling in Engineering & Sciences 2004, 5(1), 45-62. https://doi.org/10.3970/cmes.2004.005.045

Abstract

A method is developed based on an additive modification to the first Lagrangian elasticity tensor to make the finite element method for hyperelasticity viable at the atomic length scale in the context of lattice statics. Through the definition of an overlap region, the close-ranged atomic interaction energies are consistently summed over the boundary of each finite element. These energies are subsequently used to additively modify the conventional material property tensor that comes from the second derivative of the stored energy function. The summation over element boundaries, as opposed to atom clusters, allows the mesh and nodes to be defined independently from the atoms. The method is developed with a specific form of the Tersoff-Brenner potential for carbon. The method correctly predicts the in-plane deformation behavior of a single graphite sheet subjected to displacement boundary conditions. Estimated plane elasticity properties agree with experimental data from the literature. Quenched molecular dynamics results are used to validate the method for homogeneous and inhomogeneous loading constraints.

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Keywords

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