Mechanics theories for anisotropic or composite materials

Whereas mechanics theories for isotropic materials have been almost matured, those for anisotropic or composite materials well established are only limited to linear elasticity. All of the other mechanical properties of a composite outside linear elastic range are overall lack of efficient methods to deal with. Specifically, prediction of various composite failures still remains one of the biggest challenges in solid mechanics. A fundamental reason is in that only homogenized stresses are definable and obtainable for the composite by the existing theories, and the resulting stresses in its constituent fiber and matrix materials are homogenized values as well. The mechanical properties of the composite must be estimated on a true stress level. The composite true stress theory has been systematically established by this author. Besides, a number of other analytical theories have been established by the author as well. They include the unified elastic-inelastic constitutive and internal stress evaluation theory for a composite reinforced with any continuous fibers, short fibers or particles, the incremental constitutive model for a hyperelastic material, the interlaminar matrix stress modification method for prediction of interlaminar fracture or delamination in any laminated structure, and the physics based failure criteria to detect matrix dominated composite failures. Using these theories and incorporated with a finite element approach, essentially any failure and ultimate strength of a composite structure subjected to an arbitrary static, dynamic or fatigue load can be efficiently predicted with no iteration and with a minimum number of input data all of which can be measured independently and following existing standards, as long as the void content of the composite structure can be neglected. A summary on the establishment of these theories, a complete list of the explicit formulae for them, and their applications to resolve a number of challenging problems in composite failures is presented in this paper. An Excel-table based program for achieving all the true stresses conversions is attached as a supplement. Future trends in further development on mechanics of composites are highlighted. [GRAPHICS] .