A Multi-scale Formulation for Predicting Non-linear Thermo-electro-mechanical Response in Heterogeneous Bodies

Abstract

This study presents a multi-scale formulation for analyzing coupled heat conduction and thermo-electro-mechanical deformation in heterogeneous bodies, namely active composites. The studied active composite comprises ferroelectric inclusions dispersed in polymer matrix. The multi-scale framework is derived based on an integrated simplified micromechanical and finite element model. A non-linear thermo-electro-elastic constitutive model of materials undergoing large electric driving fields and small strains is used for the polarized ferroelectric inclusions. An integration algorithm with predictor and corrector schemes is developed to obtain approximate solutions of field variables: temperature, displacement, strain, stress, electric field, and electric displacement. The multi-scale model is capable of determining field variables at multiple length scales which is important when non-linear behaviors in the constituents of heterogeneous bodies are considered. We examine the effect of mismatches in the properties of the constituents in an active composite on the overall field coupling responses in the composite. We also compare the field coupling responses in an active composite to those of a homogeneous body, i.e., lead zirconate titanate (PZT). We finally present a simulation of controlling deformation in a smart cantilever beam using the multiscale framework.

Deformations of flexible and foldable electro-active composite structures

“…This approach leads to nonlinear equations for which an incremental and iterative solution is used. (26) where G is time-dependent relaxation tensor of the material. As we deal with a plane stress condition two scalar indices are considered, , , , , i j k l x y .…”

“…He formulated an electro-mechanical constitutive model by considering higher order terms of the electric field in order to describe the nonlinear electromechanical coupling behavior of piezoelectric ceramics. A limited number of studies have considered nonlinear electro-mechanical response of piezoelectric materials due to large electric fields [24][25][26], but for small deformations. Mollayousef [27] and Ben Atitallah et al [28,29] have studied material characterization of AFC under a wider range of electro-mechanical inputs.…”

The electric, magnetic, and elastic fields in damaged thermo-electro-magneto-elastic composites created by heat flow

“…To that end, we mention the articles by Shen and Kuang (1998), Lu et al (1998), Qin (1998), Liu et al (2000), Qin’s articles referenced in chapter 4 of Qin (2001), and the paper by Gao et al (2002). A multiscale formulation for the analysis of coupled heat conduction and thermo-electro-mechanical deformation in heterogeneous bodies has been presented by Muliana and Lin (2011).…”

Improvement of TFT-LCD's polarizer plate bubble problem using a preheating-process

“…Niculita found that maximum stress variation versus extension presents a short increase up to a maximum extension, and, from this peak value, this variation decreases in resin composite laminates [11]. Muliana and Lin proposed a multiscale formulation for analyzing coupled heat conduction and thermo-electro-mechanical deformation in heterogeneous active composites [12]. Philipp et al considered that front end bending in plate rolling will reduce productivity eventually, entailing expensive downtime [13].…”