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Structural systems are consistently encountering the variabilities in material properties, undesirable defects and loading environments, which may potentially shorten their designed service life. To ensure a reliable structural performance, it is vital to track and quantify the effects of different random/uncertainty factors upon the structural fracture performance. In this research, a critical review of the past, current and future computational modelling of the non-deterministic fracture mechanics is presented. By considering the variously numerical solutions tackling the fracture problems, they are mainly categorized into the discrete and continuous approaches. This study discusses the quantification performance of the extended finite element method, the crack band method and the phase-field approaches combined with different sources of uncertainties. These well-known computational techniques are typical representatives of the common fracture modelling philosophies including the embedded, smeared and regularized ones. The essence of this work is to compare the main differences of the uncertainty quantification models (i.e., probabilistic, non-probabilistic) at the fracture formulation levels and investigate the major progress and challenges existing in the real-life applications for the past and future decades. Some critical remarks, which are denoting the advantages and major issues of various non-deterministic fracture models, are provided and explained in the practical structural failure conditions. Different fracture simulation cases are implemented with comparative results amongst analytical, numerical and experimental methods, and the corresponding fracture quantification ability is evaluated through the standards of the random fracture capacity, load–deflection plots, crack propagation, crack mechanisms, and computational efficiency, etc.
Feng et al. (2023) studied this question.