r5.03.37 Homogenization of periodic heterogeneous structures

Summary:

The hypotheses and methods used in command CALC_MATE_HOMO [U4.43.07] are presented, which calculates homogenized linear thermal and thermoelastic properties for heterogeneous periodic structures with rectangular steps with base cells that have symmetries with respect to orthogonal planes in Cartesian space. The case with hexagonal symmetry can also be treated.

A table of homogenized linear thermal and thermoelastic coefficients is obtained that can be used to define orthotropic equivalent materials, which can be parameterized by control variables, such as temperature or irradiation.

All thermal and thermoelastic corrector fields are also produced, in order to allow subsequent exploitation in order to reconstitute the complete localized solution at the microscopic scale from the macroscopic solution.

• 1. Introduction
• 2. Assumptions
• 3. Methods
  • 3.1. Three-dimensional linear thermal homogenization
  • 3.2. Homogenization in three-dimensional linear thermoelasticity
  • 3.3. Homogenization and linear elasticity of Love-Kirchhoff plates in membrane-flexure
• 4. Results
  • 4.1. Three-dimensional linear thermal homogenization
  • 4.2. Homogenization in three-dimensional linear thermoelasticity
  • 4.3. Homogenization and linear elasticity of Love-Kirchhoff plates in membrane-flexure
• 5. Examples
  • 5.1. laminated elastic plate
• 6. Bibliography