The numerical modeling of failure mechanisms in plates and shells due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. In this paper, we extend ideas recently outlined in [1, 2] towards the phase field modeling of fracture in dimension-reduced continua with application to Kirchhoff plates and shells. The introduction of history fields, containing the maximum reference energy obtained in history, provides a very transparent representation of the coupled balance equations and allows the construction of an extremely robust operator split technique. The performance of the proposed models is demonstrated by means of representative numerical examples. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
[1]
Christian Miehe,et al.
Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations
,
2010
.
[2]
Christian Miehe,et al.
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
,
2010
.
[3]
Eugenio Oñate,et al.
Rotation-free triangular plate and shell elements
,
2000
.
[4]
Francisco Armero,et al.
Finite element methods for the multi-scale modeling of softening hinge lines in plates at failure
,
2006
.
[5]
Ted Belytschko,et al.
Analysis of fracture in thin shells by overlapping paired elements
,
2006
.