Analysis of strain-limiting models in solid mechanics

by · Sep 25, 2014 · 1 346 views ·

Miroslav Bulíček, Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic Elastic solids with strain-limiting response to external loading represent an interesting class of material models, capable of describing stress concentration at strains with small magnitude. We investigate mathematical properties of static deformations for such strain-limiting nonlinear models and show the main mathematical difficulties of the model that implicitly guarantees only the L1 bound for the Cauchy stress tensor. We discuss the role of the boundary conditions and for certain huge class of models we show the existence and uniqueness of the renormalized weak solution and consequently also of the weak solution.

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