Phase field method for simulating the brittle fracture of fiber reinforced composites

An asynchronous variational integrator for the phase field approach to dynamic fracture

“…It is observed that the cracks propagate from the pre‐crack tips and toward each other in a curved shape. This crack pattern was also observed in References 68 and 69.…”

A mixed-mode dependent interface and phase-field damage model for solids with inhomogeneities

“…Namely, each time step provides two minimisations which have to be solved: the first relation in Eq. (19), is in fact first order minimisation condition of the (convex) functional…”

“…The development continued by definition of a robust computational Phase-Field Model (PFM) with a rigorous thermodynamical background in [8][9][10]. Since then, a lot of enhancements of the phase-field algorithms appeared which tried to specify particular problems of the approach related to the characteristics of the computational model: scale parameter related to the width of the regularised crack, degradation function characterising the damage in the material [11,12], its effect on cracking process in various materials [13][14][15][16], crack nucleation conditions and subsequent processes [17][18][19][20] etc. The variety of degradation functions is frequently explained by particular material behaviour, properties of the computational approach and many times they are supported by empirical results.…”

A hybrid phase-field isogeometric analysis to crack propagation in porous functionally graded structures

“…In addition, higher-order degradation functions, including cubic [4] and exponentialtype degradation [59] functions, have been introduced to increase significantly the computational accuracy. In particular, the phase-field approach has been applied successfully to investigate the failure and damage mechanisms of composite structures, including laminated composite materials [1,50,73], and fiber-reinforced composite materials [71,74]. Although some researches using the phase-field model also address the failure problem for FGM structures [28,66], they are limited to the failure mechanism without porosity and involve using the finite element approach as a family of C 0 -continuity elements.…”