ABSTRACT
Micromechanics is a method to predict the mesoscale (homogenized) properties of heterogeneous materials using empirical, semi empirical, analytical, or numerical methods. This chapter deals exclusively with numerical methods, specifically using finite element simulation, to represent the microstructure and from that to extract the average properties of the material. Emphasis is placed on 3D micromechanics simulation that can estimate the whole set of elastic properties using a single model, rather than using a disjoint collection of models based on different assumptions to assemble the set of properties needed. An introduction to analytical micromechanics is presented to provide methods that bound the numerical solutions to be developed. These include Reuss, Voigt, periodic microstructure, and transversely isotropic averaging. Most of the chapter is devoted to numerical homogenization, that is, to micromechanics performed via finite element analysis. Periodic boundary conditions are enforced via constraint equations using a Python script. Since Abaqus implementation of tie constrains changed with the 2016 version, this issue is now explained carefully in this chapter and a new Appendix. Finally, the techniques described in this chapter are also applied to local-global analysis for 3D micro-structures and for laminated composites.
