Open Access

ARTICLE

The Molecular Dynamic Finite Element Method (MDFEM)

Lutz Nasdala¹ , Andreas Kempe¹ and Raimund Rolfes¹

1 Institute of Structural Analysis, Leibniz Universität Hannover, 30167 Hannover, Germany

Computers, Materials & Continua 2010, 19(1), 57-104. https://doi.org/10.3970/cmc.2010.019.057

Abstract

In order to understand the underlying mechanisms of inelastic material behavior and nonlinear surface interactions, which can be observed on macroscale as damping, softening, fracture, delamination, frictional contact etc., it is necessary to examine the molecular scale. Force fields can be applied to simulate the rearrangement of chemical and physical bonds. However, a simulation of the atomic interactions is very costly so that classical molecular dynamics (MD) is restricted to structures containing a low number of atoms such as carbon nanotubes. The objective of this paper is to show how MD simulations can be integrated into the finite element method (FEM) which is used to simulate engineering structures such as an aircraft panel or a vehicle chassis. A new type of finite element is required for force fields that include multi-body potentials. These elements take into account not only bond stretch but also bending, torsion and inversion without using rotational degrees of freedom. Since natural lengths and angles are implemented as intrinsic material parameters, the developed molecular dynamic finite element method (MDFEM) starts with a conformational analysis. By means of carbon nanotubes and elastomeric material it is demonstrated that this pre-step is needed to find an equilibrium configuration before the structure can be deformed in a succeeding loading step.

---

Keywords

---