Speaker
Description
Nanostructures are at the forefront of research due to their extraordinary mechanical, thermal, and chemical properties. Slender atomic arrangements, such as nanorods and nanobeams, open up possibilities for developing highly sensitive sensors. This contribution investigates these specific structures. If local effects such as vacancy defects and bond breaking or making scenarios play a role in such structures, a numerical simulation must be carried out within the framework of molecular dynamics [1]. However, as this becomes inefficient for very large nanostructures, multiscale models are developed and used. Numerous multiscale models already exist for modelling rod- and beam-like nanostructures for static and dynamic problems. These includes for example surface elasticity theory, nonlocal elasticity theory, nonlocal strain gradient theory, the Cauchy-Born rule, and the FE² method. Our focus is on the modelling of static problems using the FE² approach, based on the works of Miehe and Koch [2]. The homogenisation methods and the requirements for representative volume elements (RVE) are well established for continuous microstructures. This also applies to the context of structural elements such as beams on the macro scale (e.g. Klarmann et al. [3]). However, suitable approaches for linking atomistic micro-models with macro-level structural elements are still lacking. To address this, we propose a hierarchical multiscale model that integrates atomistic simulations on the micro-scale with structural elements, specifically Timoshenko beams, on the macro scale. The atomistic simulations are conducted within the framework of the finite element method [4][5], allowing for the incorporation of various types of atomic interactions and potentials. To ensure that the homogenised values are independent of the RVE length, new constraints are introduced. The multiscale model is validated by fully atomic simulations and compared in terms of computational speed and implementation effort.
[1] D. J. Tildesley, M. P. Allen: Computer simulation of liquids, Clarendon Oxford (1987).
[2] C. Miehe, A. Koch: Computational micro-to-macro transition of discretized microstructures undergoing small strain, Archive of Applied Mechanics 72, 300–317 (2002).
[3] S. Klarmann, F. Gruttmann, S. Klinkel: Homogenization assumptions for coupled multiscale analysis of structural elements: beam kinematics. Comput Mech 65, 635–661 (2019).
[4] J. Wackerfuß: Molecular mechanics in the context of the finite element method, Int. J. Numer. Meth. Engng. 77, 969-997 (2009).
[5] J. Wackerfuß, F. Niederhöfer: Using finite element codes as a numerical platform to run molecular dynamics simulations, Computational Mechanics 63(2), 271–300 (2019).
