Homogenization and inverse homogenization for 3D composites of complex architecture

Grant Steven (Strand7 Pty Ltd, Sydney, Australia)

Engineering Computations

ISSN: 0264-4401

Publication date: 1 June 2006



To describe the mathematics, mechanics and computer code that are involved in deriving the mechanical properties of a 3D composite material with a complicated internal architecture. To inform the reader how an application programming interface (API) can be used with a commercial FEA code to undertake the task. Finally to validate the process an demonstrate the versatility of the process.


The complex architecture of the composite is imported to an FEA environment and meshed. The special code is written in Pascal that applies six sets of constraints to simulate unit strain vectors on a cell of the composite. After six separate analyses are undertaken, the forces necessary to achieve the boundary constraints are summed to provide stresses and hence the necessary coefficients in the stress to strain relationship for the composite. After global FEA the strains in the homogenized material are used as input to the inverse homogenizer so that stress and strain levels in the individual ingredients of the composite can be calculated for the purposes of assessing failure.


The process of writing separate code to operate in conjunction with a commercial FEA code was found to be very reliable, time‐effective and can be of great benefit to engineers researching with composites.

Research limitations/implications

At this state all the materials can only be stressed within their elastic limit. There is no logical impediment to extending the algorithm to increase stresses into the non‐linear range.

Practical implications

The use of the API environment allows third parties to develop application‐specific code that overcomes the increasing generality of commercial FEA codes. The author can easily make the research available to the whole engineering and materials community without losing any intellectual property.


The practical results of this research are now freely available to the whole community and the work demonstrates in a general way how researchers can make their work available without having to write any FEA code, only the things they have researched.



Steven, G. (2006), "Homogenization and inverse homogenization for 3D composites of complex architecture", Engineering Computations, Vol. 23 No. 4, pp. 432-450. https://doi.org/10.1108/02644400610661181

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