Multiscale framework. Concept of geometry, materials, load conditions, and homogenization

Abstract The chapter describes the multiscale framework used in this book to study the fibre-reinforced composites based on a polymer matrix. The main objective is that the user becomes familiar with the framework and the models studied along the book. Three different scales are identified within the continuum mechanic approach: micro, meso, and macroscale. The geometry, materials of the constituents, and load conditions are described for each scale. Then, the bridge between scales is also studied with the computational homogenization methodology. Although the chapter introduces general concepts for new users, advanced features of the models for each scale are also discussed.

[1]  W. Van Paepegem,et al.  Multiscale approach for identification of transverse isotropic carbon fibre properties and prediction of woven elastic properties using ultrasonic identification , 2018, Composites Science and Technology.

[2]  O. T. Nguyen,et al.  Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior , 2002 .

[3]  Stephen R Hallett,et al.  Internal geometric modelling of 3D woven composites: A comparison between different approaches , 2015 .

[4]  Katinka Ridderbos,et al.  The coarse-graining approach to statistical mechanics: how blissful is our ignorance? , 2002 .

[5]  Elio Sacco,et al.  Variational methods for the homogenization of periodic heterogeneous media , 1998 .

[6]  J. Nédélec,et al.  Thin elastic and periodic plates , 1984 .

[7]  Conor T. McCarthy,et al.  A combined experimental–numerical approach for generating statistically equivalent fibre distributions for high strength laminated composite materials , 2010 .

[8]  V. Kouznetsova,et al.  Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme , 2002 .

[9]  L. Godoy,et al.  Evaluation of cross-ply laminate stiffness with a non-uniform distribution of transverse matrix cracks by means of a computational meso-mechanic model , 2018 .

[10]  Peter Gudmundson,et al.  Matrix crack induced stiffness reductions in [(0(m)/90(n)/+theta(p)/-theta(q))(s)](m) composite laminates , 1995 .

[11]  D. Blackketter,et al.  Micromechanics prediction of the transverse tensilc strength of carobn fiber/epoxy composites: The influence of the matrix and interface , 1993 .

[12]  Pedro P. Camanho,et al.  Numerical simulation of the non-linear deformation of 5-harness satin weaves , 2012 .

[13]  V. G. Kouznetsova,et al.  Multi-scale computational homogenization: Trends and challenges , 2010, J. Comput. Appl. Math..

[14]  Carlos González,et al.  Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: Microscopic mechanisms and modeling , 2007 .

[15]  Stepan Vladimirovitch Lomov,et al.  A progressive damage model of textile composites on meso-scale using finite element method: static damage analysis , 2014 .

[16]  Pedro P. Camanho,et al.  Generation of random distribution of fibres in long-fibre reinforced composites , 2008 .

[17]  Christophe Geuzaine,et al.  Imposing periodic boundary condition on arbitrary meshes by polynomial interpolation , 2012 .

[18]  Frank Abdi,et al.  Micromechanics-based progressive failure analysis prediction for WWFE-III composite coupon test cases , 2013 .

[19]  C. Miehe,et al.  Computational micro-to-macro transitions of discretized microstructures undergoing small strains , 2002 .

[20]  M. Pindera,et al.  Micro-macromechanical analysis of heterogeneous materials: Macroscopically homogeneous vs periodic microstructures , 2007 .

[21]  Pedro P. Camanho,et al.  Micro-mechanical analysis of the in situ effect in polymer composite laminates , 2014 .

[22]  W. Paepegem,et al.  Material parameter identification of the elementary ply damage mesomodel using virtual micro-mechanical tests of a carbon fiber epoxy system , 2017 .

[23]  W. Van Paepegem,et al.  Consistent application of periodic boundary conditions in implicit and explicit finite element simulations of damage in composites , 2019, Composites Part B: Engineering.

[24]  N. P. Dijk,et al.  A study on the influence of boundary conditions in computational homogenization of periodic structures with application to woven composites , 2017 .

[25]  W. Van Paepegem,et al.  Mesoscale analysis of ply-cracked composite laminates under in-plane and flexural thermo-mechanical loading , 2019, Composites Science and Technology.

[26]  W. Paepegem,et al.  Avoiding interpenetrations and the importance of nesting in analytic geometry construction for Representative Unit Cells of woven composite laminates , 2016 .

[27]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[28]  F. Naya,et al.  Computational micromechanics of the transverse and shear behavior of unidirectional fiber reinforced polymers including environmental effects , 2017 .

[29]  T. Massart,et al.  Bending effect on the risk for delamination at the reinforcement/matrix interface of 3D woven fabric composite using a shell-like RVE , 2012 .

[30]  E. Barbero.  Introduction to Composite Materials Design , 1998 .