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A thin sheet clamped at opposite ends and stretched develops wrinkles parallel to the direction of the applied tensile strain due to the hindered Poisson lateral contraction at the clamps. To study this phenomenon, a variational model recently proposed by Puntel, Deseri and Fried is adopted. The relevant energy functional includes bending and membranal contributions and is minimized subject to a constraint on the area of the mid-surface of the sheet. A fourth order partial-differential equation is henceforth obtained and numerically implemented using B-splines. Predictions are obtained concerning the number of wrinkles, critical applied stretches, and scaling relationships for wrinkle amplitude and wavelength. Both a linearized version of the boundary-value problem based on the small-slope approximation and a fully nonlinear one are considered: their results are found to be in good agreement for the whole range of applied stretches taken into account. Comparisons with previous analytical results by Puntel, Deseri and Fried, who used different boundary conditions and an Ansatz on the deflection function are also provided. The numerical results substantially confirm the validity of the analytical predictions. The present work provides then an alternative numerical method for the study of wrinkling in thin sheets and supports the use of analytical and semi-analytical solutions as viable options for specific geometries. Though further investigation, particularly experimental, is still needed, extensive comparisons of the results with other studies available in the literature provide confirmation for the scaling laws and signal that predicted values of the critical stretches may only be accurate for higher length-to-width aspect ratios.

We present a continuum model for thermally induced volume transitions in stimulus–responsive hydrogels (SRHs). The framework views the transition as proceeding via the motion of a sharp interface separating swollen and collapsed phases of the underlying polymer network. In addition to bulk and interfacial force and energy balances, our model imposes an interfacial normal configurational force balance. To account for the large volume changes exhibited by SRHs during actuation, the governing equations are developed in the setting of finite-strain kinematics. The numerical approximations to the coupled thermomechanical equations are obtained with an extended finite element/level-set method. The solution strategy involves a non-standard operator split and a simplified version of the level-set update. A number of representative problems are considered to investigate the model and compare its predictions to experimental observations. In particular, we consider the thermally induced swelling of spherical and cylindrical specimens. The stability of the interface evolution is also examined.

We consider a recent experiment of Kundler and Finkelmann (Macromol. Rapid Commun. 16 (1995) 679), who subjected an aligned specimen of nematic elastomer to uniaxial extension and observed the formation of striped domains. In so doing, we apply the general theory for nematic elastomers developed by Anderson et al. (J. Elast. 56 (1999) 33) and work with an energy density that combines the effects included in the molecular-statistical theory of nematic rubber elasticity with the Oseen–Zocher–Frank theory of nematic curvature elasticity. Assuming that the deformation and orientation fields remain in-plane, we arrive at a boundary-value problem which admits solutions corresponding to striped states. We use elementary aspects of bifurcation theory to explore the local stability of these solutions. We also obtain analytical estimates for the energy and thickness of interstripe domain walls as functions of imposed extension and compare these with numerical predictions.

We present a numerical study of the elastic properties of bulk nanocrystalline materials based on a continuum theory, introduced by Fried and Gurtin (2009) , for nanoscale polycrystalline elasticity that captures length-scale effects and accounts for interactions across grain boundaries via interface and junction conditions. The theory involves a balance equation containing fourth-order gradients of the displacement field. A relatively inexpensive, non-conforming finite-element method based on C 0 -continuous basis functions is presented. We develop the variational form of the method and establish consistency. The formulation weakly enforces continuity of derivatives of the displacement field across interelement boundaries and stabilization is achieved via Nitsche’s method. Based on this approach, numerical studies are performed for a polycrystal subject to an uniaxial deformation. Results indicate that the theory predicts lower Young’s modulus for bulk nanocrystalline materials than for conventional coarsely-grained polycrystals. Moreover, as the grain size decreases below a certain threshold, the effective elastic modulus decreases and the effective Poisson’s ratio increases. The distribution of the effective stress shows that the theory captures high strain gradients in the vicinity of the grain boundaries and triple junctions.