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First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks

Rudoy, Evgeny
Shcherbakov, Viktor

Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.

Sponsor
Gefördert im Rahmen des Projekts DEAL
Citation
In: Applied Mathematics & Optimization Volume 84 / Issue 3 (2020-11-16) , S. 2775-2802; eissn:1432-0606
Collections
@article{doi:10.17170/kobra-202109064714,
  author    ={Rudoy, Evgeny and Shcherbakov, Viktor},
  title    ={First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks},
  keywords ={510 and 620 and Kirchhoff-Love plate theory and Einschluss and Grenzfläche and Riss and Energie and Rissausbreitung and Bruchmechanik},
  copyright  ={http://creativecommons.org/licenses/by/4.0/},
  language ={en},
  journal  ={Applied Mathematics & Optimization},
  year   ={2020-11-16}
}