The failure criteria of long fiber composites subjected to compressive forces can be due to two main reasons, fiber buckling and/or composite delamination. A special formulation has been developed to predict this last failure mode. The fiber buckling phenomenon is included into the serial/parallel mixing theory by modifying the constitutive performance of the composite constituent materials (fiber and matrix) according to the micro-structural interaction that exist between them. The modification of the constitutive performance of both components is made using an homogenization method based on the existing analogy between the micro-structural performance of the RVE of a fiber embedded in a matrix (such the one shown in the image), and the analytical solution of a curved bar under unilateral elastic restrain.

The homogenized constitutive equations are included in an algorithm that do not only provides the compression strength of composite materials made of long fibers with initial misalignments but goes a step further, taking into account all possible situations that can be found in the numerical simulation of structures. The algorithm takes into account the direction of the stresses applied to the fibers: compression or tension, and is capable to obtain the composite performance when it is unloaded.