Back to main page

Typical experimental measurements are made by stretching clamped thin sheets. The presence of the clamps induces nonuniform stretches in the sample, but the effects of spatial stress inhomogeneity have been up to now neglected. Analogously, the observation of microstructure formation only in some parts of the sample (Zubarev et al., 1999) is not explained by an analysis restricted to macroscopically homogeneous strains.

The fingerprint of the liquid-like response at small stretches is a the flat force-displacement curve. The computed plots illustrate the presence of a sharp transition from the soft response at small stretches to a rubber-like response at larger stretches for two different values of the aspect ratio. The critical strain is significantly reduced with respect to the value in the macroscopically affine approximation which is typically used to interpret experimental results, expecially at the smaller aspect ratio.

The microstructure index distringuishes the regions where microstructure is formed (blue) from the ones where it is not (red). At small stretches the entire sample is in the liquid region, at higher stretches, only an island containing microstructure (in the smectic phase, see below) survives, and it is confined around the central part of the clamps.

The von Mises stress vanishes at small stretches, and is nonzero all across the sample at large stretches. At intermediate stretches, the stress transmission path corresponds to an X with kinked legs. The presence of the kink is related to the transmission of tensile stresses in the smectic island (compare previous Figure).

The distribution of the macroscopic gradients in the phase diagram shows the presence of many points well inside the smectic phase. All points in the smectic phase are almost exactly on a line of constant smallest principal strain, due to the fact that the energy in phase Sm is a convex function of the smallest principal strain alone. This plot corresponds to the intermediate stretch of the previous figures, s=1.38.

The colors represent the microstructure index; the circles represent the blow-up of a possible reconstruction of the local microstructure.