Development of a 4-node finite element for the computation of nano-structured materials

The molecular structure of a material determines its mechanical, thermal and chemical properties. Thus, to better understand characteristic mechanical properties like damping behavior or softening, in principle, one just has to model the interactions of a sufficiently large number of atoms. Various force field approaches have been proposed for that purpose, which are based on molecular-dynamic simulations, or rather quantum-mechanical ab initio calculations. They provide the potential energy of a structure in dependence of sort and number of chemical and physical bonds. In general, the different energy forms can be represented by nonlinear normal, bending and torsional springs which suggests the use of a finite element code. However, standard finite elements like truss, beam or shell elements are not very applicable because of the interaction of many atoms and, considered from a mechanical perspective, the absence of rotational degrees of freedom. For example, a bending of beam elements would lead to unrealistic constraints of neighboring molecular groups. In order to overcome this disadvantage, a new 4-node finite element is introduced, which uses only translational degrees of freedom and therefore is capable of representing the different energy forms exactly.