Efficient micromechanical analysis of fiber-reinforced composites subjected to cyclic loading through time homogenization and reduced-order modeling

Abstract

In this paper, a number of techniques used to accelerate the solution of finite element problems involving a large number of load cycles areexplored and applied to the micromechanical analysis of fiber-reinforced composites. The microscopic domain consists of unidirectional linear-elastic fibers embedded in a viscoelastic/viscoplastic polymeric matrix. Time homogenization is applied to divide the original equilibrium problem in macro- and microchronological parts. The size of the problem is further reduced by a combination of Proper Orthogonal Decomposition (POD) and the Empirical Cubature Method (ECM), resulting in a hyper-reduced model. A novel technique for history recovery combining Gappy Data reconstruction with a k-means clustering algorithm is proposed, as well as an adaptive strategy combining time homogenization and POD without an offline training phase. The performance of each acceleration technique is assessed and the resultant speed-ups obtained by combining them are presented.