Composites and laminates

•  Continuum mechanics, linear elasticity (see 1^st year Mechanics course)
•  Beam and plate models (see 3^rd year Thin structures and instabilities course)

•  Discover the different types of composite materials and their implementation
•  Acquire the methods of calculation of structures in composite materials
•  Master the notion of anisotropy in linear elasticity
•  Know how to replace a heterogeneous medium by an equivalent homogeneous medium (micro-macro approaches) in a modeling approach
•  Master the concepts of modeling laminates (plate models)
•  Know how to analyze the failure criteria specific to heterogeneous materials

•  General information on composite materials:
  -- constituents: inclusions, fibres, resins, fabrics
  -- processing: molding, pultrusion, centrifugation, filament winding
  -- finished products: laminates, plates and sandwich beams
•  Elastic behavior of heterogeneous media:
  -- notion of representative volume element (RVE) and equivalent homogeneous behavior
  -- characterization of the RVE (random and periodic media) and anisotropic elasticity
  -- homogenization methods (Voigt, Reuss, effective moduli, periodic homogenization, estimates and bounds of Hashin and Shtrickman) and implementation in a FE code (Abaqus)
•  Failure modes and criteria of laminates (maximum stress, maximum strain, Tsai-Hill, Hoffman, Tsai-Wu)
•  Models of laminated and sandwich plates
•  Applications to the design of composite structures

•  Know a range of materials and their potential for different applications
•  Use models of heterogeneous materials
•  Define simplified models of heterogeneous materials for efficient calculations
•  Be able to propose innovative material models

•  DS : written evaluation  2 h (75 %)
•  CC : Reports on Practical Work (25 %)

•  Course slides
•  M. Bornert, T. Bretheau et P. Gilormini, Homogénéisation en mécanique des matériaux, tomes 1 et 2, Hermes, 2001
•  J.-M. Berthelot, Matériaux composites : comportement mécanique et analyse des structures, Tec&Doc, 1999
•  D. Gay, Matériaux composites, Hermes, 1991

Stéphane Bourgeois