Development of a new variational model of crack propagation

Development of a new variational model of crack propagation

Twenty years ago, continuum modeling of crack propagation has seen a turning point through the development of variational approaches based on phase-field formalism. In this framework, a crack is described by an auxiliary field locally inducing the damage of a material which behaves elsewhere as an elastic medium. This field is explicitly involved in the free energy of the system, adjusted to control both its profile close to the damaged zone and the fracture energy.

Numerically, the phase-field approach allows the straightforward coupling of  crack propagation to other phenomenon such as the formation of solid precipitates for which comparable mathematical models have already been developed. It therefore paves the way for multi-physics modeling that is also needed to describe material behaviors more exhaustively.

However for cracks, the introduction of an additional field raises difficulties related to its coupling with the displacement field. This is because this field is the fundamental degree of freedom in which, theoretically, the physical non-linearities related to the onset of fracturing would have to be based on.

The purpose of this work is to develop a new variational model of crack propagation which would only be based on displacement fields and the formulation of a suitable elastic energy (Landau theory). The proposed model will be numerically implemented and compared to classical phase-field approaches. It should be used in studies involving the damage of nickel-base superalloys.

job : intership (3 to 6 months between January and July 2021)

Location : LEM, Châtillon

Expertise: Knowledge in solid state physics and/or material science, Capability in programing under unix/linux environment with scientific languages

Academic degree : Master degree

Contacts : Antoine Ruffini, Alphonse Finel (Email Us)