^{1}, Lori Graham-Brady

^{2}, Michael D. Shields

^{3}, David Brandyberry

^{4}and Philippe Geubelle

^{5}

^{1}Graduate Student, Dept. of Civil Engineering, Johns Hopkins University, Baltimore, United States of America

^{2}Professor, Dept. of Civil Engineering, Johns Hopkins University, Baltimore, United States of America

^{3}Assistant Professor, Dept. of Civil Engineering, Johns Hopkins University, Baltimore, United States of America

^{4}Graduate Student, Dept. of Aerospace Engineering, Universty of Illinois at Urbana Champaign, Urbana, United States of America

^{5}Professor, Dept. of Aerospace Engineering, Universty of Illinois at Urbana Champaign, Urbana, United States of America

Composite materials are multiphase materials (two or more) where the properties of the individual phases combine together to produce a strong and stiff but light material. This has led to their use in many challenging structural applications over the last few decades. However, the individual phases possess physical properties that have inherent spatial randomness. This, along with the randomness in the geometrical parameters like fiber radius, fiber inclination, etc. in fiber-reinforced matrix composites contributes to the randomness in the bulk properties of the composite. Thus, there is a need to account for the uncertainties in the bulk properties corresponding to the uncertainties in the input randomness. Fiber-reinforced composite material models are often complex and computationally expensive to solve. Thus for efficient uncertainty propagation, the total number of full model evaluations needs to be as few as possible. Uncertainty propagation can be used as an effective tool for multi-scaling such that the characterized bulk properties at the given length scale (micro-scale in this case) can be used as an input for the next higher length scale model. In this work, we consider fiber-matrix interface damage in a multi-fiber composite model where the damage parameters for each interface are assumed to be random. The goal here is to characterize the final reaction force for a given input strain with respect to different interface damage parameter values in the fibers. Using an Interface-Enriched Generalized Finite Element Method (IGFEM), the force as well as the sensitivities of the force with respect to the damage parameters can be estimated. It is of interest here to investigate whether the additional gradient information can be used to more efficiently build an accurate surrogate model representing the reaction force. In this study, the performance of two hierarchical space filled designs, namely Refined Latinized Stratified Sampling (RLSS) and Hierarchical Latin Hypercube Sampling (HLHS) are compared when used with radial basis function interpolation with or without gradients on 2-dimensional problems.