Whereas mechanics theories for isotropic materials are almost matured, only linear elastic theories for composites were essentially established. This is because only homogenized or approximated stresses are obtainable for a composite. Its mechanical properties must be estimated on a true stress level. According to Eshelby, the true stresses of the fiber are the same as its homogenized counterparts. The true stress theory for the matrix was systematically established by the author, and is reviewed and summarized in the paper. An Excel table-based program for calculating all of the possible true stress components is provided as a supplement for the reader to download. As most composite failures are caused by matrix failures, the true stress theory plays a predominant role in estimating the composite properties outside a linear elastic range. Some challenging composite failures were resolved upon the matrix true stresses, and are highlighted in the paper.
Keywords: composites; failures; stress concentrations; true stress.