A Variational Homogenization Approach on Large Strain Micro‐Electro‐Mechanics

A Variational Homogenization Approach on Large Strain Micro‐Electro‐Mechanics Functional materials have received a lot of attention in recent years. Composite materials of soft polymers with embedded ferroelectric particles are advantageous due to the large deformations possible in such materials. Phenomenological modeling of associated electromechanical coupling phenomena has been extensively covered. However, complex multi‐scale interactions based on a microscopic electric domain evolution and its effect on the overall macroscopic response is of utter importance for the understanding of the underlying physical phenomena. This necessitates the use of multi‐scale approaches such as computational homogenization to reliably predict and in turn enhance the overall material response. We propose a variational framework for micro‐electro‐mechanical response at large deformations embedded into a scale‐bridging scenario by using homogenization techniques in order to define the macroscopic overall response of electro‐active materials. Starting point is a rate‐type saddle‐point variational principle on the microscale yielding the Euler‐Lagrange equations and a Ginzburg‐Landau‐type evolution equation for the polarization order parameter. A challenge is to link the gradient‐type continuum description of the microstructure to a local electro‐mechanical macro‐continuum. This is achieved by exploiting a generalized Hill‐Mandel macro‐homogeneity condition, yielding periodic boundary conditions at the faces of the microstructure. Numerical examples demonstrate the capabilities of the framework and show the effect of particle interactions based on evolving electric domains on the overall macroscopic response. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

A Variational Homogenization Approach on Large Strain Micro‐Electro‐Mechanics

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Publisher
Wiley
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710255
Publisher site
See Article on Publisher Site

Abstract

Functional materials have received a lot of attention in recent years. Composite materials of soft polymers with embedded ferroelectric particles are advantageous due to the large deformations possible in such materials. Phenomenological modeling of associated electromechanical coupling phenomena has been extensively covered. However, complex multi‐scale interactions based on a microscopic electric domain evolution and its effect on the overall macroscopic response is of utter importance for the understanding of the underlying physical phenomena. This necessitates the use of multi‐scale approaches such as computational homogenization to reliably predict and in turn enhance the overall material response. We propose a variational framework for micro‐electro‐mechanical response at large deformations embedded into a scale‐bridging scenario by using homogenization techniques in order to define the macroscopic overall response of electro‐active materials. Starting point is a rate‐type saddle‐point variational principle on the microscale yielding the Euler‐Lagrange equations and a Ginzburg‐Landau‐type evolution equation for the polarization order parameter. A challenge is to link the gradient‐type continuum description of the microstructure to a local electro‐mechanical macro‐continuum. This is achieved by exploiting a generalized Hill‐Mandel macro‐homogeneity condition, yielding periodic boundary conditions at the faces of the microstructure. Numerical examples demonstrate the capabilities of the framework and show the effect of particle interactions based on evolving electric domains on the overall macroscopic response. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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