Probabilistic approach in modelling dynamic fracture problems

Abstract

The paper represents a probabilistic approach to the finite element modelling of dynamic fracture problems. It is proposed to model internal structural defects and inhomogeneities using the spatial distribution of strength characteristics according to the normal distribution law. The probabilistic approach to modelling dynamic fracture is provided by the introduction of one additional parameter – the dispersion in the distribution of strength material properties. This approach provides the probabilistic nature to the initiation and development of cracks in the material at any scale level: macro, meso and micro level. There are no restrictions on the size of computational mesh and elements, the fracture criterion and the material models to apply this approach. The probabilistic approach is also applicable to multilevel modelling using the appropriate distribution of inhomogeneities. This approach does not require a detailed study of the material structure, which enhances the predictive nature of computations. The numerical results of exploding cylinder tests and the penetration of thin targets by a projectile are presented. Numerical results are in good qualitative and quantitative agreement with experimental data.