WIAS Preprint No. 2299, (2016)

Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach


  • Kraus, Christiane
  • Radszuweit, Markus

2010 Mathematics Subject Classification

  • 74F05 74F20 74N20 74R20 74S05 80A17

2008 Physics and Astronomy Classification Scheme

  • 02.70.Dh 62.20.mt 64.70.kd 64.75.Op 65.40.De


  • Damage, Fracture, Phase field model, Binary alloys, Thermo-mechanics, Spinodal decomposition, Finite Element


We present a continuum model that incorporates rate-dependent damage and fracture, a material order parameter field and temperature. Different material characteristics throughout the medium yield a strong inhomogeneity and affect the way fracture propagates. The phasefield approach is employed to describe degradation. For the material order parameter we assume a Cahn Larché-type dynamics, which makes the model in particular applicable to binary alloys. We give thermodynamically consistent evolution equations resulting from a unified variational approach. Diverse coupling mechanisms can be covered within the model, such as heat dissipation during fracture, thermal-expansion-in- duced failure and elastic-inhomogeneity effects. We furthermore present an adaptive Finite Element code in two space dimensions, that is capable of solving such a highly nonlinear and non-convex system of partial differential equations. With the help of this tool we conduct numerical experiments of different complexity in order to investigate the possibilities and limitations of the presented model. A main feature of our model is that we can describe the process of micro-crack nucleation in regions of partial damage to form macro-cracks in a unifying approach.

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