Perturbation-based stochastic finite element analysis of the interface defects in composites via Response Function Method

The main aim of this paper is to present a mathematical model and its numerical realization for the composite material with stochastic interface defects employing the perturbation-based stochastic finite elements. The defects are modeled as the semicircular micro-cavities (“bubbles”) lying with their diameters on the reinforcement-matrix interface inside the weaker material region (matrix). Both total number of the defects as well as their radii may be defined as the truncated Gaussian random variables with the given first two probabilistic moments. The composite micro-geometry is simulated according to these parameters and the entire structure is discretized in both scales using traditional Finite Element Method procedures. Its probabilistic version is provided thanks to the Response Function Method, where several numerical tests with random parameter values varying around its mean value 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 shear test for the carbon–epoxy composite with the few interface defects and Young modulus of the matrix being Gaussian random variable, where three meshes with various density show overall convergence of the numerical procedure.