TY  - JOUR
T1  - Analysis and approximation of a strain-limiting nonlinear elastic model
A1  - Bulíček, Miroslav
A1  - Málek, Josef
A1  - Süli, Endre
JA  - Mathematics and Mechanics of Solids
Y1  - 2015
VL  - 20
IS  - 1
SP  - 92–118
M2  - doi: 10.1177/1081286514543601
N2  - 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.
M1  - Preprint project = MORE
M1  - Preprint year = 2013
M1  - Preprint number = 05
M1  - Preprint ID = MORE/2013/05
ER  -