Heat source generated by crack propagation/damage growth in the phase field damage model

[ngrilli]

Description of the enhancement or error report

We currently have the phase field damage model implemented in the Kernel SplitPFFractureBulkRate and in the Material LinearIsoElasticPFDamage. However, when the phase field damage model is coupled with temperature (HeatConductionTimeDerivative and HeatConduction), it is necessary to add the heat source given by the dissipation due to crack propagation (damage growth) in order to be thermodynamically consistent. This heat source is given by: Q = - (dPsi / dc) (dc / dt), where c is the damage phase field and Psi is the free energy: Psi = (1 - c)^2 G0_pos + G0_neg, where G0_pos and G0_neg are the positive and negative components of the specific strain energies.

C. Miehe, L.M. Schänzel, H. Ulmer, Comput. Methods Appl. Mech. Engrg. 294 (2015) 449–485 http://www.sciencedirect.com/science/article/pii/S0045782514004423

P. Chakraborty, Y. Zhang, M.R. Tonks, Multi-scale modeling of microstructure dependent inter-granular fracture in UO2 using a phase-field based method Idaho National Laboratory technical report https://inldigitallibrary.inl.gov/sites/sti/sti/6360441.pdf

Rationale for the enhancement or information for reproducing the error

Necessity of a heat source for the dissipation due to crack propagation/damage growth to be thermodynamically consistent

Identified impact

Add another Kernel CrackPropagationHeatEnergy and another Material ComputeCrackPropagationHeatEnergy (similar to what was done for the energy dissipation due to plastic deformation)

[MartimSalgado]

Why wasn't this model pushed? It looks like a very important contribution!

[ngrilli]

Dear @MartimSalgado

The code for the heat source given by damage propagation is available in this repository: https://github.com/ngrilli/Marisol

It is documented in the following paper: https://aip.scitation.org/doi/abs/10.1063/1.5030656

Best Regards, Nicolò Grilli