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SUMMARY:Duvan Henao (Instituto de Ciencias de la Ingeniería\, Universidad
  de O’Higgins)
DTSTART:20250408T120000Z
DTEND:20250408T130000Z
DTSTAMP:20260411T211117Z
UID:FunctionSpaces/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FunctionSpac
 es/105/">NeoHookean energies\, cavitation\, and relaxation in nonlinear el
 asticity</a>\nby Duvan Henao (Instituto de Ciencias de la Ingeniería\, Un
 iversidad de O’Higgins) as part of Function spaces\n\n\nAbstract\nThe ne
 oHookean model is one of the most commonly used approaches to study the me
 chanical response of elastic bodies undergoing large deformations. However
 \, the neoHookean energy is expected to possess no minimizers in the Sobol
 ev class naturally associated to its quadratic coercivity. This is connect
 ed to the formation and sudden expansion of voids observed in confined ela
 stomers. There is analytical evidence for the conjecture that the nonexist
 ence is due to the opening of an ever larger number of cavities. Regulariz
 ations of the neoHookean model either impose a length-scale for the caviti
 es created (with a second gradient\, or taking into account the energy req
 uired to stretch the created surface) or impose a bound in the number of c
 avities that the body is allowed to open. In the second approach\, the fir
 st existence results are due to Henao & Rodiac (2018) in the axisymmetric 
 class for hollow domains\, and to Doležalová\, Hencl & Molchanova (2024)
  in the weak closure of homeomorphisms in 3D. In more general classes wher
 e harmonic dipoles are admitted\, a relaxation approach has been proposed 
 by Barchiesi\, Henao\, Mora-Corral & Rodiac (2023\, 2024)\, where the mass
  of the singular part of the derivative of the inverse is found to accurat
 ely give the cost of creating dipole singularities.\n
LOCATION:https://researchseminars.org/talk/FunctionSpaces/105/
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