On numerical aspects of phase field fracture modelling
Materials and Process Simulation, University of Bayreuth, Bayreuth, Germany
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Revised: 29 August 2011
Accepted: 22 September 2011
Published online: 26 October 2011
Recently, a continuum model for crack propagation in brittle visco-elastic materials has been presented (M. Fleck et al., Phys. Rev. E 83, 046213 (2011)), in which fracture is described as an elastically induced nonequilibrium interfacial pattern formation process. The underlying mesoscopic description of a propagating crack results in a complicated moving boundary problem, that allows the self-consistent determination of the crack velocity as well as the entire time-dependent crack surface. Here we focus on the numerical aspects tied to the approximative solution of the arising moving boundary problem and discuss several strategies to develop efficient numerical schemes applying to it: i) a finite difference scheme, ii) a scheme based on the finite element method and iii) a scheme based on the multipole expansion method. The pros and cons of each method are elucidated in detail. Further, we present a comprehensive view on how the different approaches can be employed to validate each other in comparative studies, which is then illustrated for the example of crack propagation under mode I loading.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2011