Disorder, pre-stress and non-affinity in polymer 8-chain models

To assess the role of single-chain elasticity, non-affine strain fields and pre-stressed reference states we present and discuss the results of numerical and analytical analyses of modified 8-chain Arruda-Boyce model for cross-linked polymer networks. This class of models has proved highly successful in modeling the finite-strain response of flexible rubbers. We extend it to include the effects of spatial disorder and the associated non-affinity, and use it to assess the validity of replacing the constituent chain's nonlinear elastic response with equivalent linear, Hookean springs. Surprisingly, we find that even in the regime of linear response, the full polymer model gives very different results from its linearized counterpart, even though none of the chains are stretched beyond their linear regime. We demonstrate that this effect is due to the fact that the polymer models are under considerable pre-stress in their ground state. We show that pre-stress strongly suppresses non-affinity in these unit cell models, resulting in a marked stiffening of the bulk response. The effects of pre-stress we discuss may explain why fully affine mechanical models, in many cases, predict the bulk mechanical response of disordered stiff polymer networks so well.Comment: 29 pages, 7 figures. Submitted to J. Mech. Phys. Solid

Le mythe, les représentations et le culte du dirigeant dans la Roumanie communiste

Québec Université Laval, Bibliothèque 201

Valence states of iron ions in nanostructured yttrium iron garnet Y3FE5O12 studied by means of soft X-ray absorption spectroscopy

Nanostructured samples of yttrium iron garnet Y3Fe5O12 obtained by plastic deformation method (high-pressure torsion) were studied with help of soft X-ray absorption spectroscopy using Fe 2p and O 1s spectra. Experimental spectra were compared with crystal field multiplet calculations for Fe ions. Some amount of Fe2+ ions in nanostructured Y3Fe5O12 was found. The concentration of Fe2+ ions was found to be increased with the increase of the degree of plastic deformatio