Atomistic to continuum coupling in solid mechanics

par Eduard Marenic

Thèse de doctorat en Mécanique

Sous la direction de Adnan Ibrahimbegovic.

Thèses en préparation à Cachan, Ecole normale supérieure , dans le cadre de École doctorale Sciences pratiques (1998-2015 ; Cachan, Val-de-Marne) depuis le 01-05-2012 .

  • Résumé

    Over the past three decades, we have acquired new tools and techniques to analyse and synthesize nanoscale objects and learn their many incredible properties. These advances have stimulated ever broader research activities in science and engineering devoted entirely to the study and applications of materials on nano-scale, termed nanomechanics. Nanomechanics or nanotechnology is making, and will continue to make, an impact in key areas for societal improvement. analysis and During the last decade, research effort in the field of numerical modeling of the deformation process is dedicated to the study of the mechanical behavior of materials on micro and nano scale. Nano-mechanics emerged from this effort and it is typically associated with the study of the mechanical behavior of a group of atoms or atomic scale systems. Even though advantages and drawbacks of the engineering material reside on fundamental, nano scale, it is often impossible to model the whole domain of the problem with nano resolution. The restrictive parameter is today's computer power which is not adequate, and that is the reason why multi-scale (MS) coupled atomistic/continuum methods are developed. The key idea of such approach is to use macroscopic continuum mechanics which is less accurate but inherently cheaper for the most of the problem domain. On a small part of interest (e.g. around crack tip) molecular dynamics (MD) or molecular mechanics (MM) is used, however at the cost of solving an equation for each single atom/molecule. Two main problems arise near and on the interface when trying to achieve coupling of the local continuum and non-local atomistic models. The first one is the appearance of the so-called ghost forces. As the name suggests, this phenomenon is related to the creation of spurious forces, in the coupling area, induced by the incompatibility in local and non-local mathematical models. A consequence of this is inaccurate simulation and the impossibility of keeping a state of equilibrium in the material. The second spurious effect is the reflection of mechanical waves at the interface between the two models. Basically, the coupling might not allow displacement waves to travel correctly. In particular, the interface between the two models produces wave reflections which perturb the propagation of kinetic energy. The main focus of the research is on the improvement of the atomistic-to-continuum simulation of solids by quenching the spurious effects. The first objective is a quantitative analysis of the ghost forces induced by the Bridging domain (BD) method (introduced by T. Belitschko, S. Xiao) and by the Quasicontinuum (QC) method (introduced by E.B. Tadmor). This analysis should ultimately give the means of suppressing these forces, and similar approach should be performed in dynamic simulation.

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