Multiscale stochastic modeling of the failure of fiber reinforced composites

A crucial characteristic of complex materials is randomness and uncertainty in their constituent elements, in distribution of defects, and in interactions among them. For realistic complex materials systems characterized by inherent randomness, various types of errors, and/or incompletely measured data across scales, innovative modeling is required to effectively integrate stochastic methods into the multiscale framework. In this study the socalled multiscale stochastic modeling (MSM) method is proposed for probabilistic failure prediction of unidirectional fiber reinforced polymer composites. The mechanism-based, bottom-up hierarchical MSM consists of two upscaling processes: 1) In the micro-to-meso process, fiber statistical strength, randomness in fiber-matrix debonding and random distribution of fibers is investigated using the shear lag model and 3D finite elements. The concept of stochastic representative volume element (SRVE) is introduced as an intermediate vehicle to transport microstructural statistics to full-scale structural reliability solutions. A unique feature of the simulation is that probabilistic strength and associated fracture energy of the SRVE can be assessed simultaneously. 2) The statistics of the SRVE are used as input for the meso-to-macro upscaling process. Based on stochastic continuum damage mechanics, nonlinear stochastic finite element analysis is implemented. For highdimensional reliability problems, efficient schemes such as multi-resolution nonlinear finite elements, sparse grids, and arc-length based advanced reliability methods can be specially developed.

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