WIAS Preprint No. 2359, (2016)

Linearized elasticity as Mosco-limit of finite elasticity in the presence of cracks


  • Gussmann, Pascal
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 35J85 49J40 74B20 74A45


  • Gamma convergence, Mosco convergence, finite-strain elasticity, rigidity estimate for, crack domains, global injectivity, local non-interpenetration condition




The small-deformation limit of finite elasticity is considered in presence of a given crack. The rescaled finite energies with the constraint of global injectivity are shown to Gamma converge to the linearized elastic energy with a local constraint of noninterpenetrability along the crack.

Appeared in

  • Adv. Calculus Variations, 13 (2020), pp. 33--52 (published online on 17.10.2017), DOI 10.1515/acv-2017-0010 .

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