# A multi-material level set-based topology optimization of flexoelectric composites

## TL;DR

This paper introduces a computational methodology for multi-material topology optimization of flexoelectric composites, enabling the design of complex multi-phase structures with improved electromechanical properties.

## Contribution

It extends previous single-material methods to multi-material designs using a multi-phase level set model and advanced PDE discretization techniques.

## Key findings

- Demonstrates flexibility with 2-4 phase designs
- Achieves significant enhancement in electromechanical coupling
- Validates the methodology with numerical examples

## Abstract

We present a computational design methodology for topology optimization of multi-material-based flexoelectric composites. The methodology extends our recently proposed design methodology for a single flexoelectric material. We adopt the multi-phase vector level set (LS) model which easily copes with various numbers of phases, efficiently satisfies multiple constraints and intrinsically avoids overlap or vacuum among different phases. We extend the point wise density mapping technique for multi-material design and use the B-spline elements to discretize the partial differential equations (PDEs) of flexoelectricity. The dependence of the objective function on the design variables is incorporated using the adjoint technique.The obtained design sensitivities are used in the Hamilton Jacobi equation to update the LS function. We provide numerical examples for two, three and four phase flexoelectric composites to demonstrate the flexibility of the model as well as the significant enhancement in electromechanical coupling coefficient that can be obtained using multi-material topology optimization for flexoelectric composites.

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Source: https://tomesphere.com/paper/1901.10752