Axisymmetric bifurcations of thick spherical shells under inflation and compression

Incremental equilibrium equations and corresponding boundary conditions for an isotropic, hyperelastic and incompressible material are summarized and then specialized to a form suitable for the analysis of a spherical shell subject to an internal or an external pressure. A thick-walled spherical shell during inflation is analyzed using four different material models. Specifically, one and two terms in the Ogden energy formulation, the Gent model and an I1 formulation recently proposed by Lopez-Pamies. We investigate the existence of local pressure maxima and minima and the dependence of the corresponding stretches on the material model and on shell thickness. These results are then used to investigate axisymmetric bifurcations of the inflated shell. The analysis is extended to determine the behavior of a thick-walled spherical shell subject to an external pressure. We find that the results of the two terms Ogden formulation, the Gent and the Lopez-Pamies models are very similar, for the one term Ogden material we identify additional critical stretches, which have not been reported in the literature before

Optimal energy-harvesting cycles for load-driven dielectric generators in plane strain

The performances of energy harvesting generators based on dielectric elastomers are investigated. The configuration is of a thin dielectric film coated by stretchable electrodes at both sides. The film is first stretched, then charged and subsequently, afterwards it is released, and finally the charge is harvested at a higher electric potential. The amount of energy extracted by this cycle is bounded by the electric breakdown and the ultimate stretch ratio of the film as well as by structural instabilities due to loss of tension. To identify the optimal cycle that complies with these limits we formulate a constraint optimization problem and solve it with a dedicated solver for two typical classes of elastic dielectrics. As anticipated, we find that the performance of the generator depends critically on the ultimate stretch ratio of the film. However, more surprising is our finding of a universal limit on the dielectric strength of the film beyond which the optimal cycle is independent of this parameter. Thus, we reveal that, regardless of how large the dielectric strength of the material is, there is an upper bound on the amount of harvested energy that depends only on the ultimate stretch ratio. We conclude the work with detailed calculations of the optimal cycles for two commercially available elastic dielectrics

Analytical and numerical analyses of the micromechanics of soft fibrous connective tissues

State of the art research and treatment of biological tissues require accurate and efficient methods for describing their mechanical properties. Indeed, micromechanics motivated approaches provide a systematic method for elevating relevant data from the microscopic level to the macroscopic one. In this work the mechanical responses of hyperelastic tissues with one and two families of collagen fibers are analyzed by application of a new variational estimate accounting for their histology and the behaviors of their constituents. The resulting, close form expressions, are used to determine the overall response of the wall of a healthy human coronary artery. To demonstrate the accuracy of the proposed method these predictions are compared with corresponding 3-D finite element simulations of a periodic unit cell of the tissue with two families of fibers. Throughout, the analytical predictions for the highly nonlinear and anisotropic tissue are in agreement with the numerical simulations

Effective properties of nonlinear inhomogeneous dielectrics

We develop a general procedure for estimating the effective constitutive behavior of nonlinear dielectrics. The procedure is based on a variational principle expressing the effective energy function of a given nonlinear composite in terms of the effective energy functions of the class of linear comparison composites. This provides an automatic procedure for converting well-known information for linear composites, in the form of estimates and bounds for their effective dielectric constants, into corresponding estimates and bounds for the effective behavior of nonlinear composites. Further, the procedure is easily implemented, and leads in some cases to exact results. This, exact estimates are given herein for isotropic weakly nonlinear composites with general nonlinearity, and bounds of the Hashin-Shtrikman type are given for the class of two-phase, isotropic dielectric composites with strongly and perfectly non-linear constitutive behavior. The optimality of the bounds is addressed briefly