Stochastic failure analysis of structures with softening materials

Stochastic modelling of crack propagation in materials with random properties using isometric mapping for dimensionality reduction of nonlinear data sets

“…Sample functions of a Weibull distributed stochastic field for standard deviation 5 × 10 −2 and l c equal to 1.2 and 15 mm are shown in Figure . It is clear how a higher degree of heterogeneity is given not only by a higher standard deviation in input, but also by a lower correlation length, as observed in the study of Carmeliet and Hens . Figure shows the crack patterns obtained for 4 realisations with 2 different degrees of standard deviation (0.1 × 10 −2 and 5 × 10 −2 ) and 2 different correlation lengths (1.2 and 15 mm).…”

“…It is clear how a higher degree of heterogeneity is given not only by a higher standard deviation in input, but also by a lower correlation length, as observed in the study of Carmeliet and Hens. 40 Figure 20 shows the crack patterns obtained for 4 realisations with 2 different degrees of standard deviation (0.1 × 10 −2 and 5 × 10 −2 ) and 2 different correlation lengths (1.2 and 15 mm). It is worth noticing that in the case with higher spatial variability, the crack paths show an extremely tortuous pattern compared with the others.…”

A non-local probabilistic method for modeling of crack propagation

“…Although multi-scale modelling has been proved to be a powerful method for incorporation of the heterogeneity, difficulties may arise when a detailed knowledge of the material micro-structure for identifying the representative elementary volume, is not available. For this reason, an increasing interest has now been directed towards stochastic approaches, as they allow probabilistic estimation of degree of heterogeneity in the materials by quantifying fluctuations of mechanical properties [3][4][5][6]46].…”

On adaptive refinements in discrete probabilistic fracture models

“…Availability of adaptive refinement allows starting simulation with coarse discretization and refining it adaptively during the simulation run only in areas where needed. T In some applications of fracture simulations, it might be important to consider additional material randomness (besides the one covered by the random location of nodes in the discrete model) usually represented by a random field [15][16][17][18]. An extension of the discrete model by fluctuation of material parameters according to a random field was developed in [18,19].…”