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Phase Field Modeling of Brittle and Ductile Fracture
Author(s) -
Ulmer Heike,
Hofacker Martina,
Miehe Christian
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310258
Subject(s) - classification of discontinuities , brittleness , finite element method , phase field models , fracture mechanics , complex fracture , brittle fracture , materials science , field (mathematics) , fracture (geology) , phase (matter) , mechanics , phase transition , structural engineering , physics , engineering , composite material , mathematics , mathematical analysis , thermodynamics , quantum mechanics , pure mathematics
The phase field modeling of brittle fracture was a topic of intense research in the last few years and is now well‐established. We refer to the work [1‐3], where a thermodynamically consistent framework was developed. The main advantage is that the phase‐field‐type diffusive crack approach is a smooth continuum formulation which avoids the modeling of discontinuities and can be implemented in a straightforward manner by multi‐field finite element methods. Therefore complex crack patterns including branching can be resolved easily. In this paper, we extend the recently outlined phase field model of brittle crack propagation [1‐3] towards the analysis of ductile fracture in elastic‐plastic solids . In particular, we propose a formulation that is able to predict the brittle‐to‐ductile failure mode transition under dynamic loading that was first observed in experiments by Kalthoff and Winkler [4]. To this end, we outline a new thermodynamically consistent framework for phase field models of crack propagation in ductile elastic‐plastic solids under dynamic loading, develop an incremental variational principle and consider its robust numerical implementation by a multi‐field finite element method. The performance of the proposed phase field formulation of fracture is demonstrated by means of the numerical simulation of the classical Kalthoff‐Winkler experiment that shows the dynamic failure mode transition. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)