Common Misconceptions on Rules of Mixtures
Please pardon me if I am preaching to the choir here. Rules of mixtures (ROM) are very simple mechanics models. Everybody on this site has a very good understanding of it. However, confusion and mistakes on ROM constantly appear in textbooks, journal articles, online learning materials, etc. See attached two wiki articles. The major confusing point is that vf*Ef+vm*Em is derived from the isostrain assumption and the upper bound. Both statements are incorrect. There might be two main reasons contributed to this mistake/confusion.