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: Part I deals with
all "ingredients" to start with multi-scale modelling, limited to
elastic property prediction. This typically includes: (i) setting
up your geometrical model at micro- or meso-scale (definition of
Representative Volume Element (RVE) or Repeating Unit Cell (RUC)),
(ii) definition of periodic boundary conditions, (iii)
homogenization of the elastic properties, starting from the elastic
properties of the constituents, (iv) importance of statistical
representation of geometry and stochastic nature of fibre
architecture. This should bring all readers at the same level of
principles and terminology for multi-scale modelling. Advanced
users could eventually skip this first part. Part II deals with
nonlinear multi-scale modelling. We build further upon the
ingredients from Part I, but now add all kinds of nonlinearities to
the simulation at micro- or meso-scale (matrix cracking,
delamination, fibre/matrix debonding, delamination, fibre failure,
visco-elasto-plasticity-damage of the polymer matrix,...). Not only
finite element based techniques are covered, but also much faster
inclusion methods (Mori-Tanaka, Eshelby,...) and variational
methods. Part III deals with the laminate scale or macro-scale,
where all these multi-scale modelling tools are applied for
macro-scale ply-based modelling and virtual testing of laminates
(in static loading, but also sometimes for prediction of fatigue,
post-impact strength,...). In all three parts, the main three types
of fibre reinforcement are covered (unidirectionally reinforced
composites, textile composites and short fibre composites). The
chapters are written by leading authorities from academia, and each
chapter gives a self-contained overview of a specific topic,
covering the state-of-the-art and future research challenges.
General
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