Experimental tests of entanglement models of rubber elasticity. 3. Biaxial deformations

Gottlieb, Moshe; Gaylord, Richard J.

doi:10.1021/ma00167a022

Cited by 46 publications

(43 citation statements)

References 12 publications

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“…23,24,[31][32][33] Better accuracy can be realized using a general form of the strain energy function suggested by Rivlin. 22 The curvature in the stress-strain response is captured to some extent by molecular theories of rubber deformation, such as the constraint models, [34][35][36][37][38][39][40] which include the effect of topological interactions on the microscopic deformation. However, these models still tend to overestimate the stress for compression.…”

Section: Resultsmentioning

confidence: 99%

Strains in an Inflated Rubber Sheet

Mott

Roland

Hassan

2003

Rubber Chemistry and Technology

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A technique to measure the strain distribution of an inflated membrane is described, and applied to natural rubber inflated to pole biaxial strains of 12%, 26%, and 33%. The radial strain was found to be nearly constant over the entire surface, while the circumferential strain falls to zero at the edge. Thus, biaxial deformation is limited to a narrow region in the vicinity of the pole. These results are quite different from (the very limited) data published previously. The stressstrain behavior was also measured in uniaxial tension, and the strain distribution of the inflated membrane calculated using finite elements. The experiment results and the modeling were in good agreement.

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Section: Resultsmentioning

confidence: 99%

Strains in an Inflated Rubber Sheet

Mott

Roland

Hassan

2003

Rubber Chemistry and Technology

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“…As we have already pointed out, the worst approach is probably to rely on a fit of rheological data to the stress-strain curves that follow from equation (25) regarding γ as a parameter characterizing the average confinement of whatever modes. Judging from the inconclusiveness of previous investigations along these lines [31][32][33][34][35][36][37], it is clear that more microscopic input is needed. But even neutron scattering experiments [29,30,47] are limited to comparing the data to structure factors calculated from models.…”

Section: Discussionmentioning

confidence: 99%

“…That the importance of entanglements is still sometimes disputed is due to the inconclusiveness of rheological experiments [31][32][33][34][35][36][37]. It is very complicated to prepare well-characterized model systems and to relate experimental data to structural properties or to analytical theory in a unique way.…”

Section: Introductionmentioning

confidence: 99%

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

Everaers

1998

Eur. Phys. J. B

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Abstract. We present a new model of rubber elasticity where linear forces act to constrain the fluctuations of the eigenmodes of the phantom model. The model allows us to treat the constrained junction and the tube model within the same, transparent formalism, does not require any further approximations, and is particularly suited for the analysis of simulation data for (strained) model polymer networks. As an interesting side result we show that in order for the model to be consistent, the constraints (but not the mean polymer conformations!) have to deform affinely, a severe restriction that might also apply to other models. Complementary, we prove in analogy to the derivation of the virial theorem that introducing constraints into the phantom network Hamiltonian leads to extra terms in addition to the usual Doi-Edwards formulas for the polymer contribution to the stress tensor which vanish only for affinely deforming constraints.

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“…(31) and (32) are constants, so it does not realistically describe the uniaxial or biaxial stretching of even isotropic rubbers [32,36,37]. Consequently the values of coefficients fitted to experiments are likely to be only approximate.…”

Section: B Smectic Layer Buckling Finite Extensibility and Entanglmentioning

confidence: 99%

Numerical study of stretched smectic-Aelastomer sheets

Brown

Adams

2013

Phys. Rev. E

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We present a numerical study of stretching monodomain smectic-A elastomer sheets, computed using the finite element method. When stretched parallel to their smectic layer normal the smectic layers are unstable to a transition to a buckled state. We model macroscopic deformations by replacing the microscopic energy with a coarse grained effective free energy that accounts for the fine-scale layer buckling. We augment this model with a term to describe the energy of deforming buckled layers, which is necessary to reproduce the experimentally observed Poisson ratios postbuckling. We examine the spatial distribution of the microstructure phases for various stretching angles relative to the layer normal and for different length-to-width aspect ratios. When stretching parallel to the layer normal the majority of the sample forms a bidirectionally buckled microstructure, except at the clamps where a unidirectionally buckled microstructure is predicted. When stretching at small inclinations to the layer normal the phase of the sample is sensitive to the aspect ratio of the sample, with the bidirectionally buckled phase persistent to large angles only for small aspect ratios. We relate these theoretical results to experiments on smectic-A elastomers.

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Experimental tests of entanglement models of rubber elasticity. 3. Biaxial deformations

Cited by 46 publications

References 12 publications

Strains in an Inflated Rubber Sheet

Strains in an Inflated Rubber Sheet

Constrained fluctuation theories of rubber elasticity: General results and an exactly solvable model

Numerical study of stretched smectic-Aelastomer sheets

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