دانلود رایگان مقاله فرآیند همگن سازی دو مقیاسی محاسباتی الکترو الاستیسیته در سویه محدود

Abstract

This contribution addresses a two-scale computational homogenization framework for the simulation of electro-active solids at finite strains. A generalized form of the Hill–Mandel condition is employed for the derivation of energetically consistent transition conditions between the scales. The continuum mechanical formulation is implemented into a two-scale finite element environment, in which we attach a microscopic representative volume element at each integration point of the macroscopic domain. In order to allow for an efficient solution of the macroscopic boundary value problem an algorithmically consistent tangent of the macroscopic problem is derived. The method will be applied to the analysis of dielectric polymer–ceramic composites, where we determine the effective actuation of composites with different microstructures. Furthermore, we show the applicability of the proposed method to the computation of two-scale electro-mechanically coupled boundary value problems in consideration of large deformations.

5. Summary and conclusion

We have presented a two-scale finite-element (FE2 ) framework for the simulation of electro-elastic materials at finite strains. The method was derived based on classical micro–macro transition conditions for electro-mechanical fields. The microscopic boundary value problem was defined on periodic representative volume elements. In order to account for the effect of electrostatic volume forces we employed the concept of Maxwell stress on the microscale. The overall macroscopic response was computed by suitable averaging processes over the microscale. The presented method was then applied to the simulation of electro-elastic polymer-matrix composites with ceramic inclusions. The influence of the inclusion’s dielectric properties on the overall coupling was analyzed in detail. In addition to that, different volume fractions of circular as well as ellipsoidal inclusions were studied. The simulations confirmed that the actuation performance of a soft polymer can significantly be enhanced by adding ceramic dispersions. Here, next to electric properties and volume fraction, the shape of the inclusion has shown a major influence on the overall actuation. This reveals the inclusion shape as an important design variable for the development of dielectric composites with enhanced properties. Finally, we applied the framework to the two-scale simulation of an electro-mechanical boundary value problem given by an electric bimorph actuator. The simulations showed that the method can be used for the detailed study of electro-elastic coupling phenomena of soft materials at finite deformations on two separate scales.