Multiscale Modeling of Complex Materials. Phenomenological, Theoretical and Computational Aspects
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 ty...
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Modal Analysis of Nonlinear Mechanical Systems
The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attentio...
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Separated Representations and PGD-Based Model Reduction Fundamentals and Applications
The papers in this volume start with a description of the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a new generation of simulation strategies based on the use of separated representations (space-parameters, space-t...
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Collective Dynamics from Bacteria to Crowds
Multiscale models in social applications combine mean-field and kinetic equations with either microscopic or macroscopic level descriptions. In this book the reader will find not only a wide spectrum of multiscale analysis results (like convergence proofs), but also practically important information such as derivations of mean-field equations, methods to handle hard contacts numerically, to mod...
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Constitutive Relations under Impact Loadings
The book describes behavior of materials (ductile, brittle and composites) under impact loadings and high strain rates. The three aspects: experimental, theoretical and numerical are in the focus of interest. Hopkinson bars are mainly used as experimental devices to describe dynamic behavior of materials. The precise description of experimental techniques and interpretation of wave interaction ...
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