Introduction to Micromechanics

By Wenbin Yu

Purdue University

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This article provides a brief introduction to micromechanics using linear elastic materials as an example. The fundamental micromechanics concepts including homogenization and dehomogenization, representative volume element (RVE), unit cell, average stress and strain theories, effective stiffness and compliance, Hill-Mandel macrohomogeneity condition. This chapter also describes the detailed derivations of the rules of mixtures, and three full field micromechanics theories including finite element analysis of a representative volume element (RVE analysis), mathematical homogenization theory (MHT), and mechanics of structure genome (MSG). It is shown that RVE analysis with periodic boundary conditions is exactly the same as MHT. This equivalency implies that it is unnecessary to  implement MHT in a special purpose code as commercial finite element software packages can be readily to achieve this purpose. MSG can reproduce the same equations for MHT but can have a much more efficient implementation due to its inherent variational nature.