An adaptive stochastic multi-scale method for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension

Abstract

An adaptive stochastic multi-scale method is developed for cohesive fracture modelling of quasi-brittle heterogeneous materials under uniaxial tension. In this method, a macro-domain is first discretised into a number of non-overlapping meso-scale elements (MeEs) each of which containing detailed micro-scale finite element meshes. Potential discrete cracks in the MeEs are modelled by pre-inserted cohesive interface elements (CIEs). Nonlinear simulations are conducted for the MeEs to obtain the crack patterns under different boundary conditions. The macro-domain with the same number of overlapped, adaptively size-increasing MeEs are then simulated, until the potential cracks seamlessly cross the boundaries of adjacent MeEs. The resultant cracks, after being filtered by a new Bayesian inference algorithm to remove spurious cracks wherever necessary, are then integrated as CIEs into a final anisotropic macro-model for global mechanical responses. A two-dimensional example of carbon fibre reinforced polymers was modelled under two types of uniaxial tension boundaries. The developed method predicted crack patterns and load–displacement curves in excellent agreement with those from a full micro-scale simulation, but consuming considerably less computation time of the latter.