Mechanics of composite materials

Mathematical formalism for the representation of elasticity tensors in anisotropy


Design of composite material structures (stiffness and/or strength properties)

Mechanics of deformable solids

Introduction

Definition of a composite material
Manufacturing processes
Application examples


Ply scale

Anisotropy and representation methods

Hooke's law for anisotropic materials
Tensor notations, Voigt and Pedersen notations
Physical significance of elastic components
Elastic symmetries, 3D reference frame rotation
The plane state of stress
Invariant representations : Tsai and Pagano parameters, polar parameters


Heterogeneity and homogenization of elastic properties

Representative elementary volume
Law of mixtures
Reuss and Voigt bounds
Hashin and Shtrikman model
Halpin and Tsai model
Contiguity equations


Strength criteria for anisotropic materials

Maximum stress
Maximum strain
Tsai-Hill
Hoffman
Tsai-Wu
Hashin
Puck




Laminate scaling

The classical theory of laminates

The kinematic model
The fundamental law of laminates, inversion of the law
Elastic moduli of the equivalent monolayer
Thermo-elastic behavior
The case of identical-layer laminates
The use of invariant representations


Types of laminates used in industrial applications

Decoupled
balanced
Angle-ply
Cross-ply
Quasi-isotropic
Isotropic
Quasi-homogeneous


Calculation of shear stresses
Free edge stresses
Reissner- theoryMindlin theory
Higher-order theories
Pagano's 3D theory


Classical laminate design

Laminate parameters
Miki's method
Stiffness design
Strength design
Numerical approaches


Optimal laminate design

Formulation of the laminate design problem as an optimization problem
The different approaches : direct and two-stage (multiscale) formulation
Optimal design in stiffness

Use of the polar method to formulate/solve the stiffness optimization problem
Analytical solution for an orthotropic plate


Optimal design in strength

Invariant formulation of strength criteria with the polar method
Formulation of the strength optimization problem
Analytical solution for an orthotropic plate

Inorganic Chemistry and Materials