Rules of mixtures (ROM) might be the simplest composite mechanics models. However, in many books, papers, and online learning materials, it is incorrectly claimed that the simple rule of mixture E1V1+E2V2 provides upper bound for the Young's modulus (see https://en.wikipedia.org/wiki/Rule_of_mixtures, https://en.wikipedia.org/wiki/Composite_material). This is only true if Poisson's effects are neglected. Otherwise, the correct upper bound will be larger than this formula. Another mistake is that it is commonly believed that this simple formula is derived from isostrain assumption, which is wrong too. It is actually derived from isostrain assumption in one direction and isostress (or zero Poission's ratio) assumption in other directions. Feel free to let me know your comments. I recently wrote a tutorial note for educational purpose to clarify these misconceptions along with other confusing points on rules of mixtures.
Article Common Misconceptions on Rules of Mixtures for Predicting El...
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