This book presents the state-of-the-art in multiscale modeling and simulation techniques for composite materials and structures. It focuses on the structural and functional properties of engineering composites and the sustainable high performance of components and structures. The multiscale techniques can be also applied to nanocomposites which are important application areas in nanotechnology. There are few books available on this topic.

Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples. The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then passes to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green’s tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory. Bridges theory and practice, providing step-by-step instructions for implementing multiscale modeling approaches for composites and the theoretical concepts behind them Covers boundary conditions, data-exchange between scales, the Hill-Mandel principle, average stress and strain theorems, and more Discusses how to obtain composite properties using different boundary conditions Includes access to a companion site, featuring the numerical examples, Python and ABACUS codes discussed in the book

Multi-scale modelling of composites is a very relevant topic in composites science. This is illustrated by the numerous sessions in the recent European and International Conferences on Composite Materials, but also by the fast developments in multi-scale modelling software tools, developed by large industrial players such as Siemens (Virtual Material Characterization toolkit and MultiMechanics virtual testing software), MSC/e-Xstream (Digimat software), Simulia (micromechanics plug-in in Abaqus), HyperSizer (Multi-scale design of composites), Altair (Altair Multiscale Designer) This book is intended to be an ideal reference on the latest advances in multi-scale modelling of fibre-reinforced polymer composites, that is accessible for both (young) researchers and end users of modelling software. We target three main groups: This book aims at a complete introduction and overview of the state-of-the-art in multi-scale modelling of composites in three axes: • ranging from prediction of homogenized elastic properties to nonlinear material behaviour • ranging from geometrical models for random packing of unidirectional fibres over meso-scale geometries for textile composites to orientation tensors for short fibre composites • ranging from damage modelling of unidirectionally reinforced composites over textile composites to short fibre-reinforced composites The book covers the three most important scales in multi-scale modelling of composites: (i) micro-scale, (ii) meso-scale and (iii) macro-scale. The nano-scale and related atomistic and molecular modelling approaches are deliberately excluded, since the book wants to focus on continuum mechanics and there are already a lot of dedicated books about polymer nanocomposites. A strong focus is put on physics-based damage modelling, in the sense that the chapters devote attention to modelling the different damage mechanisms (matrix cracking, fibre/matrix debonding, delamination, fibre fracture,...) in such a way that the underlying physics of the initiation and growth of these damage modes is respected. The book also gives room to not only discuss the finite element based approaches for multi-scale modelling, but also much faster methods that are popular in industrial software, such as Mean Field Homogenization methods (based on Mori-Tanaka and Eshelby solutions) and variational methods (shear lag theory and more advanced theories). Since the book targets a wide audience, the focus is put on the most common numerical approaches that are used in multi-scale modelling. Very specialized numerical methods like peridynamics modelling, Material Point Method, eXtended Finite Element Method (XFEM), isogeometric analysis, SPH (Smoothed Particle Hydrodynamics),... are excluded. Outline of the book The book is divided in three large parts, well balanced with each a similar number of chapters:

Due to their high stiffness and strength and their good processing properties short fibre reinforced thermoplastics are well-established construction materials. Up to now, simulation of engineering parts consisting of short fibre reinforced thermoplastics has often been based on macroscopic phenomenological models, but deformations, damage and failure of composite materials strongly depend on their microstructure. The typical modes of failure of short fibre thermoplastics enriched with glass fibres are matrix failure, rupture of fibres and delamination, and pure macroscopic consideration is not sufficient to predict those effects. The typical predictive phenomenological models are complex and only available for very special failures. A quantitative prediction on how failure will change depending on the content and orientation of the fibres is generally not possible, and the direct involvement of the above effects in a numerical simulation requires multi-scale modelling. One the one hand, this makes it possible to take into account the properties of the matrix material and the fibre material, the microstructure of the composite in terms of fibre content, fibre orientation and shape as well as the properties of the interface between fibres and matrix. On the other hand, the multi-scale approach links these local properties to the global behaviour and forms the basis for the dimensioning and design of engineering components. Furthermore, multi-scale numerical simulations are required to allow efficient solution of the models when investigating three-dimensional problems of dimensioning engineering parts. Bringing together mathematical modelling, materials mechanics, numerical methods and experimental engineering, this book provides a unique overview of multi-scale modelling approaches, multi-scale simulations and experimental investigations of short fibre reinforced thermoplastics. The first chapters focus on two principal subjects: the mathematical and mechanical models governing composite properties and damage description. The subsequent chapters present numerical algorithms based on the Finite Element Method and the Boundary Element Method, both of which make explicit use of the composite’s microstructure. Further, the results of the numerical simulations are shown and compared to experimental results. Lastly, the book investigates deformation and failure of composite materials experimentally, explaining the applied methods and presenting the results for different volume fractions of fibres. This book is a valuable resource for applied mathematics, theoretical and experimental mechanical engineers as well as engineers in industry dealing with modelling and simulation of short fibre reinforced composites.

Summary: A Generalized Multiscale Analysis Approach brings together comprehensive background information on the multiscale nature of the composite, constituent material behaviour, damage models and key techniques for multiscale modelling, as well as presenting the findings and methods, developed over a lifetime's research, of three leading experts in the field. The unified approach presented in the book for conducting multiscale analysis and design of conventional and smart composite materials is also applicable for structures with complete linear and nonlinear material behavior, with numerous applications provided to illustrate use. Modeling composite behaviour is a key challenge in research and industry; when done efficiently and reliably it can save money, decrease time to market with new innovations and prevent component failure.

This book provides an overview of multiscale approaches and homogenization procedures as well as damage evaluation and crack initiation, and addresses recent advances in the analysis and discretization of heterogeneous materials. It also highlights the state of the art in this research area with respect to different computational methods, software development and applications to engineering structures. The first part focuses on defects in composite materials including their numerical and experimental investigations; elastic as well as elastoplastic constitutive models are considered, where the modeling has been performed at macro- and micro levels. The second part is devoted to novel computational schemes applied on different scales and discusses the validation of numerical results. The third part discusses gradient enhanced modeling, in particular quasi-brittle and ductile damage, using the gradient enhanced approach. The final part addresses thermoplasticity, solid-liquid mixtures and ferroelectric models. The contents are based on the international workshop “Multiscale Modeling of Heterogeneous Structures” (MUMO 2016), held in Dubrovnik, Croatia in September 2016.

Computational Mechanics of Composite Materials lays stress on the advantages of combining theoretical advancements in applied mathematics and mechanics with the probabilistic approach to experimental data in meeting the practical needs of engineers. Features: Programs for the probabilistic homogenisation of composite structures with finite numbers of components allow composites to be treated as homogeneous materials with simpler behaviours. Treatment of defects in the interfaces within heterogeneous materials and those arising in composite objects as a whole by stochastic modelling. New models for the reliability of composite structures. Novel numerical algorithms for effective Monte-Carlo simulation. Computational Mechanics of Composite Materials will be of interest to academic and practising civil, mechanical, electronic and aerospatial engineers, to materials scientists and to applied mathematicians requiring accurate and usable models of the behaviour of composite materials.