Stochastic Analysis of Composite Materials

This thesis describes the development of stochastic analysis frameworks for use in engineering design and optimisation. The research focuses on fibre-reinforced composites, with the stochastic analyses of an existing analytical failure model for unidirectional composites and of a unit cell numerical model of a 2D 5-Harness satin weave. Stochastic failure envelopes are generated through parallelised Monte Carlo Simulation of deterministic, analytical, physically based failure criteria for unidirectional carbon fibre/epoxy matrix composite plies. Monte Carlo integration of global variance-based Sobol sensitivity indices is performed and utilised to decompose observed variance within stochastic failure envelopes into contributions from physical input parameters. It is observed how the interaction effect can be used to identify domains of bi-modal failure, within which the predicted failure probability is governed by multiple failure modes. A reduced unit cell (rUC) model of a 5-Harness satin weave is constructed and analysed deterministically in uniaxial and biaxial loading conditions. An algorithm is developed and implemented to fully automate the rUC construction such that stochastic variations of the crimp angle can be evaluated. Monte Carlo Simulation is employed to propagate the effect of the crimp angle through the deterministic model and the probabilistic response compared with data obtained experimentally. It is observed how simulated variability compares well in uni-axial compression, but under-predicts observed experimental variability in uni-axial tension. The influence of vertical stacking sequence of plies is also demonstrated through the study of in-phase and out-of-phase periodic boundary conditions. The research highlights various, potential advantages that stochastic methodologies offer over the traditional deterministic approach, making a case for their application in engineering design and providing a springboard for further research come the day when greater computational power is available