Signorini problem as a variational limit of obstacle problems in nonlinear elasticity

An energy functional for the obstacle problem in linear elasticity is obtained as a variational limit of nonlinear elastic energy functionals describing a material body subject to pure traction load under a unilateral constraint representing the rigid obstacle. There exist loads pushing the body aga...

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Bibliographic Details
Published inMathematics in engineering Vol. 6; no. 2; pp. 261 - 304
Main Authors Maddalena, Francesco, Percivale, Danilo, Tomarelli, Franco
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
asymptotic analysis
calculus of variations
finite elasticity
gamma-convergence
linear elasticity
nonlinear elasticity
signorini problem
unilateral constraint
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ISSN2640-3501
2640-3501
DOI10.3934/mine.2024012

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Summary:An energy functional for the obstacle problem in linear elasticity is obtained as a variational limit of nonlinear elastic energy functionals describing a material body subject to pure traction load under a unilateral constraint representing the rigid obstacle. There exist loads pushing the body against the obstacle, but unfit for the geometry of the whole system body-obstacle, so that the corresponding variational limit turns out to be different from the classical Signorini problem in linear elasticity. However, if the force field acting on the body fulfils an appropriate geometric admissibility condition, we can show coincidence of minima. The analysis developed here provides a rigorous variational justification of the Signorini problem in linear elasticity, together with an accurate analysis of the unilateral constraint.
ISSN:2640-3501
2640-3501
DOI:10.3934/mine.2024012