Multiscale materials modeling is an effective approach for the accurate numerical study of material phenomena which occur across multiple length and time scales. Atomistic-to-continuum multiscale methods are able to drastically reduce a system’s degrees of freedom in comparison to single-scale atomistic methods. However, these methods are computationally still very demanding, which presents a major hindrance to their industrial adoption. This thesis introduces three novel approaches to improve the efficiency of these methods and shows their effectiveness in various numerical examples.The first approach is concerned with hierarchical atomistic-to-continuum multiscale methods. In these methods, the fine-scale data is often noise-corrupted due to limited computational resources. This noise impairs the convergence behavior of the multiscale method and creates a setting that shows remarkable resemblance to iteration schemes known from the field of stochastic approximation. This resemblance justifies the use of two well-known stochastic approximation averaging strategies in the multiscale method.It is found that the averaging strategies reduce the impact of the noise and improve the convergence behavior of the multiscale method.The second and third approaches are concerned with concurrent atomistic-to-continuum methods. The scales are commonly coupled at fixed intervals of time in these methods,which is often inefficient. In the second approach, a demand-based coupling is proposed instead, in order to save redundant coarse-scale computations. This coupling is achieved via a novel algorithm which continuously judges, based on the local deformation at the coupling interface, whether the coarse-scale computations are necessary or not.The continuum models in concurrent atomistic-to-continuum methods are either dynamic or quasi-static, both of which are shown to have advantages but also significant drawbacks. In the third approach, an alternative model, suitable for linear elastic continua, is presented. This hybrid model uses a complementary superposition of a dynamic and a quasi-static subproblem and aims at combining the advantages of the dynamic and quasi-static models, while avoiding the drawbacks.
|Qualifikation||Doktor der Technik|
|Datum der Bewilligung||7 Dez 2020|
|Publikationsstatus||Veröffentlicht - 7 Dez 2020|