Analytical, Numerical and Computational Multiscale Modelling Techniques for Heterogenous Materials: A Review

Abstract

This paper reviews the analytical, numerical as well as the computational homogenization multiscale modelling schemes for determining the effective material properties for heterogeneous medium at the macroscopic level. It also looked at the limitations of the analytical homogenization techniques in simulating the effective non linear heterogeneous material behaviours (for example the rapid localization of damage and so on) as well as the advancements of the computational techniques in addressing these limitations. In addition, the possible future trends for the computational technique such as the development of a fully coupled micro-macro computational scheme were also discussed. It was concluded that although, the analytical technique was quite popular and straight forward, its inability to capture rapid localization of damage limited its application and that numerical and computational schemes were able to address these limitations as they relied on the establishment of constitutive relations for the macroscopic problems in a numerical form through which the macroscopic problems were constructed and solved in a nested manner.