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Journal Articles Archive for Rational Mechanics and Analysis Year : 2018

Approximation of a Brittle Fracture Energy with a Constraint of Non-Interpenetration

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Abstract

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
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Dates and versions

hal-01584963 , version 1 (10-09-2017)
hal-01584963 , version 2 (09-11-2017)

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Antonin Chambolle, Sergio Conti, Gilles A Francfort. Approximation of a Brittle Fracture Energy with a Constraint of Non-Interpenetration. Archive for Rational Mechanics and Analysis, 2018, 228 (3), pp.867-889. ⟨10.1007/s00205-017-1207-z⟩. ⟨hal-01584963v2⟩
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