Stochastic Boundary Element Method analysis of the interface defects in composite materials

The main aim of this paper is to present a mathematical model and its numerical realization of the composite materials with stochastic interface defects. Those defects are modeled as the semicircular “bubbles” lying with their diameters on the reinforcement–matrix interface and inside the weaker material region. Both total number of the defects as well as their radii are treated as the Gaussian random variables with the given first two probabilistic moments. According to those parameters the microgeometry is simulated and the entire composite in both scales is discretized using the Boundary Element Method. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with varying values of the random parameters enable to determine the structural response and, thanks to the Least Squares Method, its final probabilistic moments. The proposed technique has been validated on the example of the carbon-epoxy composite with the few interface defects having Gaussian random radii subjected to the shear test. The presented approach may be extended towards a full 3D BEM model of the composites with stochastic interface defects as well as to provide the homogenization method for such composites using the elastostatics BEM programs.