Crack growth model

with phase field approach

( our approach )

Gradient flow model

Introduce temporal evolution of strain and phase field with gradient flow of total energy of Bourdin-Francfort-Marigo's

Extention

Rewrite energy description when new variables have relation directly to strain and phase field
Add some equations and functions with gradient flow model when new variables have relation indirectly to strain and phase field

Viscoelastic model

Rewrite elastic energy with internal strain which is described by simple model of springs and dashpots
New variable, internal strain, is deirectly coupled with original strain

Hydrogen-embrittlement model

Set function of diffusivity of Hydrogen atom and energy release rate (toughenss), and add diffusion equation of density of Hydrogen atom
New variable, number density of Hydrogen-atoms, is coupled with phase field through toughness

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