2012/07/31 by M. Hofacker, Martina Hofacker, Christian Miehé +1 · 300 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Classification of discontinuities #Composite Material Mechanics #Computer science #Displacement field #Engineering #Field (mathematics) #Finite element method #Fracture (geology) #Fracture mechanics #Geotechnical engineering #Mathematical analysis #Mathematics #Mechanics #Numerical methods in engineering #Phase (matter) #Phase field models #Physics #Structural engineering
paper · doi:10.1002/nme.4387
published in International Journal for Numerical Methods in Engineering 93(3), 276-301 (Wiley)
openalex publication_date 2012/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
SUMMARY The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. Following our recent works on quasi‐static modeling of phase‐field‐type brittle fracture, we propose in this paper a computational framework for diffusive fracture for dynamic problems that allows the simulation of complex evolving crack topologies. It is based on the introduction of a local history field that contains a maximum reference energy obtained in the deformation history, which may be considered as a measure of the maximum tensile strain in the history. This local variable drives the evolution of the crack phase field. Its introduction provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of a very robust algorithmic treatment for elastodynamic problems of diffusive fracture. Here, we extend the recently proposed operator split scheme from quasi‐static to dynamic problems. In a typical time step, it successively updates the history field, the crack phase field, and finally the displacement field. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples, which show the evolution of complex crack patterns under dynamic loading. Copyright © 2012 John Wiley & Sons, Ltd.