PSI - Issue 68

Q.M. Vuong et al. / Procedia Structural Integrity 68 (2025) 887–893 Q.M. Vuong et al. / Structural Integrity Procedia 00 (2024) 000–000

892

6

Acknowledgements

This work have been made thanks to the funding of QM Vuong’s PhD by the French embassy in Vietnam (2022-2025) through the France Excellence grant program.

Table of Notation E

- Total energy

- Elastic strain energy density

ψ ε γ u ϕ

- Deformation

- Crack surface density function

- Displacement

- Phase-field variable

G c

- Critical energy release rate - Work of the applied forces - Length scale parameter - Equivalent conductivity - Ice saturated conductivity - Liquid saturated conductivity

F l c

λ e

λ sat , i λ sat , l λ dry

- Dry conductivity

- Kersten numbers under frozen conditions - Kersten numbers under unfrozen conditions

K e f K e u S L S C

- Unfrozen water content

- Frozen ice content

- Cauchy stress

σ C

- Linear elastic sti ff ness matrix

n

- Porosity

p i p l

- Micro-ice pressure - Micro-liquid pressure

- Identity matrix

δ i j

- Poison’s coe ffi cient of solid - Poison’s coe ffi cient of ice - Young’s modulus of solid - Young’s modulus of ice

v s v i

E s E i T m

- Melting temperature

T

- Temperature

References

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