Stochastic Multiscale Modeling Of Complex Materials
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Stochastic Multiscale Modeling of Complex Materials
Multiscale modeling and simulation of complex materials is still a formidable task. The challenge arises due to the lack of scale separation in systems that exhibit nonlinear and chaotic dynamics. In this dissertation, we develop stochastic, multiscale and data-driven methods for modeling complex systems, with a focus on the dynamic compaction of heterogeneous granular materials. We first devise an energy-conserving multiscale hybrid model that explicitly accounts for macropore compaction dynamics at the mesoscale. Subsequently, we develop a probabilistic generalization that models the heterogeneous initial microstructure as a random field to explain thermal localization. The results motivate a data-driven sparse regression method to discover analytical expressions for PDF equations from Monte Carlo simulation data. This method has shown to be a promising direction for data-driven coarse-graining in a wide range of physics and engineering applications. In addition, we introduce model uncertainty and subscale fluctuations that arise due chaotic intergranular stresses through the formalism of stochastic differential equations (SDE). Finally, a hybrid algorithm that couples SDEs with PDEs is developed to combine fine- and coarse-grained probabilistic models in the same domain.
Multiscale Modeling of Complex Materials
The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.
Multiscale Modeling of Complex Molecular Structure and Dynamics with MBN Explorer
This book introduces readers to MesoBioNano (MBN) Explorer – a multi-purpose software package designed to model molecular systems at various levels of size and complexity. In addition, it presents a specially designed multi-task toolkit and interface – the MBN Studio – which enables the set-up of input files, controls the simulations, and supports the subsequent visualization and analysis of the results obtained. The book subsequently provides a systematic description of the capabilities of this universal and powerful software package within the framework of computational molecular science, and guides readers through its applications in numerous areas of research in bio- and chemical physics and material science – ranging from the nano- to the mesoscale. MBN Explorer is particularly suited to computing the system’s energy, to optimizing molecular structure, and to exploring the various facets of molecular and random walk dynamics. The package allows the use of a broad variety of interatomic potentials and can, e.g., be configured to select any subset of a molecular system as rigid fragments, whenever a significant reduction in the number of dynamical degrees of freedom is required for computational practicalities. MBN Studio enables users to easily construct initial geometries for the molecular, liquid, crystalline, gaseous and hybrid systems that serve as input for the subsequent simulations of their physical and chemical properties using MBN Explorer. Despite its universality, the computational efficiency of MBN Explorer is comparable to that of other, more specialized software packages, making it a viable multi-purpose alternative for the computational modeling of complex molecular systems. A number of detailed case studies presented in the second part of this book demonstrate MBN Explorer’s usefulness and efficiency in the fields of atomic clusters and nanoparticles, biomolecular systems, nanostructured materials, composite materials and hybrid systems, crystals, liquids and gases, as well as in providing modeling support for novel and emerging technologies. Last but not least, with the release of the 3rd edition of MBN Explorer in spring 2017, a free trial version will be available from the MBN Research Center website (mbnresearch.com).