Abstract

Dielectric elastomers are active materials that undergo large deformations and change their instantaneous moduli when they are actuated by electric fields. By virtue of these features, composites made of soft dielectrics can filter waves across frequency bands that are electrostatically tunable. To date, to improve the performance of these adaptive phononic crystals, such as the width of these bands at the actuated state, metaheuristics-based topology optimization was used. However, the design freedom offered by this approach is limited because the number of function evaluations increases exponentially with the number of design variables. Here, we go beyond the limitations of this approach, by developing an efficient gradient-based topology optimization method for maximizing the width of the band gaps in an exemplary case study. We employ a finite element formulation of the governing equations, and use the properties of each element as the design variables. In order to iteratively update the design variables, we employ gradient-based optimization, namely the Method of Moving Asymptotes. We carry out and implement fully analytical sensitivity analysis for computing the gradient of the objective function with respect to each one of the design variables. The numerical results of the method developed here demonstrate prohibited frequency bands that are indeed wider that those that were generated using metaheuristics-based topology optimization, while the computational cost to identify them is reduced by orders of magnitude.

Highlights

  • Dielectric elastomers (DEs) are active materials that undergo large deformations when they are actuated by electric fields (Pelrine et al, 2000; Hajiesmaili & Clarke, 2021)

  • To provide a self-contained report, here we briefly summarize the governing equations pertaining to nonlinear electro-mechanical deformation of dielectric elastomers following the theory of nonlinear electroelasticity (Dorfmann & Ogden, 2005; Suo et al, 2008) and the associated linearized incremental theory (Dorfmann & Ogden, 2010)

  • As mentioned, using the above theory, Shmuel (2013) determined the quasistatic deformation of the periodic DE composite owing to axial electric fields [see the study by Sharma et al (2021)], and developed the equations that govern incremental anti-plane shear waves propagating through the deformed composite

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Summary

Introduction

2021; Ortigosa & Martínez-Frutos, 2021; Khurana et al, 2021) and artificial muscles (Lu et al, 2016), that are based on DEs. The studies mentioned above aimed at optimizing the linear elastic response, while optimization techniques have been employed only recently for band gaps that depend on nonlinear elastic deformations (Hedayatrasa et al, 2016; Bortot et al, 2018; De Pascalis et al, 2020) The limitation of these three studies, from the optimal design point of view, is that they are based on metaheuristics, Genetic Algorithms (GA). The full potential of topology optimization can only be accessed if gradient-based optimization is used, so that the computational effort can be reduced by orders of magnitude and fine design resolution can be accommodated Such efficient approach is developed here for the case study analyzed by Shmuel (2013), to which Bortot et al (2018) applied GA optimization.

Governing equations
Nonlinear electroelasticity theory
The linearized incremental theory
Finite element formulation
Topology optimization
Material property interpolation for topology optimization
Optimization problem
Design sensitivity analysis
Implementation
Numerical results and discussions
Validation of the finite element framework
Topology optimization results
Findings
Summary
Full Text
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