Analysis and approximation of a strain-limiting nonlinear elastic model. (January 2015)

• Record Type: Journal Article
• Authors: Bulíček, M; Málek, J; Süli, E
• Other Names: Casey James guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 20:Number 1(2015:Jan.)
• Page Start: 92
• Page End: 118
• Publication Date: 2015-01
• Subjects: Elasticity -- linearized strain -- strain-limiting model -- first-order PDE system -- stress concentration -- spatially periodic problem -- existence of solution -- weak solution -- regularity -- uniqueness -- renormalized solutions -- Fourier spectral method; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286514543601
• Languages: English
• ISSNs: 1081-2865

Abstract

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. A theoretical justification of this class of models comes naturally from implicit constitutive theory. We investigate mathematical properties of static deformations for such strain-limiting nonlinear models. Focusing on the spatially periodic setting, we obtain results concerning existence, uniqueness and regularity of weak solutions, and existence of renormalized solutions for the full range of the positive scalar parameter featuring in the model. These solutions are constructed via a Fourier spectral method. We formulate a sufficient condition for ensuring that a renormalized solution is in fact a weak solution, and we comment on the extension of the analysis to nonperiodic boundary-value problems.