Multiscale Modeling of Buckling of Fiber-Reinforced Polymers

Fiber reinforced plastics are widely used in advanced structures such as aerospace industry, energy and automotive industries. Their advantages over conventional materials are, among others, their higher strength- and stiffness- to- weight ratio, high corrosion resistance, and adjustable mechanical properties. However, their application is limited due to different failure mechanisms such as matrix shear failure, delamination, fiber crushing and most importantly, fiber bucking (kinking) under compressive loads. In unidirectional fiber reinforced composites, fiber kinking is known as the most significant failure mechanism since it could lead to abrupt instability of the material and a drop of the load carrying capacity of the structure. Therefore, predicting the compressive strength of the structure depends on predicting the stress state at which fiber kinking happens.

Due to the difference between the size of the engineering component and the microstructure where the fiber kinking happens, using multiscale strategies are necessary. However, fiber kinking is a localized phenomenon, which makes the multiscale methods based on the global-local analysis preferable over homogenization techniques (based on RVEs) for making an admissible prediction of the failure behavior.

Hence, the Multiscale Projection Method, which has already been developed for multiscale fracture mechanics, will be adapted for fiber kinking problems. In this model we define a small fine scale area in which the microstructure of the composite material (fiber, matrix and their interface) is explicitly represented. The boundary condition for the fine scale computations is applied from the coarse scale solution as displacement values interpolated on the fine scale boundary nodes. The stress and material tangent are projected back from the fine scale to the coarse scale as effective values. The debonding between fiber and matrix is simulated using a geometrically nonlinear cohesive element which is compatible with the large rotations happening due to buckling of fibers.

The location of fine scale domain where the fiber kinking is supposed to happen is detected automatically using a proper kinking criterion.