Stochastic theory of composite materials with random waviness of the reinforcements

Abstract

A general stochastic theory of the elastic properties of composite materials with continuous randomly curved spatial reinforcement is developed. The theory of random functions is utilized to evaluate the probabilistic characteristics of the local waviness of the reinforcement. A probabilistic extension of the orientation averaging model is developed to evaluate the elastic response of composites with multidirectional reinforcement having stochastic waviness. One fundamental advantage of the developed theory, compared to existing analytical approaches, is that an exact description of the reinforcement waviness is not required for predicting elastic properties. The only essential characteristics used as input data are the mean reinforcement paths and standard deviation of the local tangent, which is a random value characterizing the reinforcement path deflection from the “perfect” one. It is shown that existing approaches for evaluating elastic response of the composite with imperfect continuous fiber reinforcement can be obtained from the developed theory as particular cases. The theory is illustrated with examples of a unidirectional composite and a helically wound composite with randomly curved reinforcements. Numerical examples show that even small local waviness of the reinforcement paths may significantly affect the elastic response of composites considered.