# The Response of Conductive-Fiber Reinforced Composites to Electric Field

## TL;DR

This paper develops an analytical model coupling electric, magnetic, thermal, and mechanical effects to predict the response of fiber-reinforced composites under electric fields, with applications in sensors and actuators.

## Contribution

It introduces a coupled analytical approach for predicting the multi-physics response of conductive-fiber composites subjected to electric fields, including computational methods and practical applications.

## Key findings

- Magnetic, thermal, and mechanical field distributions are quantitatively analyzed.
- The model predicts the composite's macroscopic response under electric excitation.
- Application to iron fiber-epoxy composites demonstrates the approach's effectiveness.

## Abstract

An analytical procedure, which couples electric, magnetic, thermal and mechanical effects is presented for the prediction of the response of unidirectional fiber-reinforced composites that are subjected to electric field, applied in the fibers' direction. It is assumed that at least one of the phases of the composite (e.g., the fibers) is electrically conductive, and that all phases are thermally conductive. The composite is assumed to occupy a finite, symmetric domain which is discretized into a double array of subcells. The governing equations, with the interfacial and boundary conditions, are satisfied in the integral sense. The externally applied field generates electric current, which induces a magnetic field as well as temperature increase. The mechanical deformation of the composite results from the combined effect of the ponderomotive force, which is created by the magnetic field, and the temperature distribution within the constituents. The purpose of the present paper is three-fold. (a) To perform quantitative analysis of the model for the ponderoromotive force in deformable media. (b) To present computational strong-form treatment of the magneto-mechanical boundary-value problem in a composite. (c) To suggest a computational apparatus for deriving the response of a sensor/actuator excited by an applied electric field or electric field gradient. Application is given, presenting the magnetic, thermal and mechanical field distributions, as well as the macroscopic (global) response of a composite, which consists, for simplicity, of two iron fibers embedded in an epoxy matrix.