Approximation of a Brittle Fracture Energy with a Constraint of Non-Interpenetration
Provides a rigorous mathematical foundation for phase-field fracture models with contact, relevant for computational mechanics and materials science.
The authors extend a Γ-convergence approximation of brittle fracture energy to include a non-interpenetration constraint, ensuring only nonnegative normal jumps are allowed. The result is a phase-field approximation that respects this physical constraint.
Linear fracture mechanics (or at least the initiation part of that theory) can be framed in a variational context as a minimization problem over a SBD type space. The corresponding functional can in turn be approximated in the sense of $Γ$-convergence by a sequence of functionals involving a phase field as well as the displacement field. We show that a similar approximation persists if additionally imposing a non-interpenetration constraint in the minimization, namely that only nonnegative normal jumps should be permissible. 2010 Mathematics subject classification: 26A45