Computational Multi‐Scale Stability Analysis of Periodic Electroactive Polymer Composites at Finite Strains

Abstract

AbstractThis work is dedicated to multi‐scale stability analysis, especially macroscopic and microscopic stability analysis of periodic electroactive polymer (EAP) composites with embedded fibers. Computational homogenization is considered to determine the response of materials at macro‐scale depending on the selected representative volume element (RVE) at micro‐scale [4, 5]. The quasi‐incompressibility condition is considered by implementing a four‐field variational formulation on the RVE, see [7]. Based on the works [1–3, 6, 8] the macroscopic instabilities are determined by the loss of strong ellipticity of homogenized moduli. On the other hand, the bifurcation type microscopic instabilities are treated exploiting the Bloch‐Floquet wave analysis in context of finite element discretization, which allows to detect the changed critical size of periodicity of the microstructure and critical macroscopic loading points. Finally, representative numerical examples are given which demonstrate the onset of instability surfaces, the stable macroscopic loading ranges, and further a periodic buckling mode at a microscopic instability point is presented. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)