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2024 | Book

Electro- and Magneto-Mechanics of Soft Solids

Constitutive Modelling, Numerical Implementations, and Instabilities


About this book

This book examines the electro- and magneto-mechanics of soft composite materials and structures, and focuses on magnetorheological elastomers (MREs) and dielectric elastomer composites (DECs), which are composite materials that comprise ferromagnetic and high-dielectric/conducting filler nano- and micro-particles embedded in a soft polymeric matrix. This gives rise to a coupled magneto- and electro-mechanical response at the macroscopic (order of millimeters and larger) scale when they are subjected to magneto- electro-mechanical external stimuli. While such MRE and DEC materials and devices can become unstable at some critical electro-magneto-mechanical loading, their response may be well controlled in the post-instability regime. Moreover, recent advances on the complete electro-magneto-mechanical coupling are presented. All those aforementioned features motivate the operation of these devices in this unstable region to obtain controlled pattern formation, soft robotic motion and artificial muscles, controllable band-gap acoustic and electromagnetic properties, energy harvesting as well as actively controlled stiffness (for cell-growth). The book contains four individual chapters covering work on the fundamentals (O. Lopez-Pamies) and the modeling (M. Gei) of electroactive solids, the modeling of magnetoactive solids (K. Danas), and the analysis of elastic instabilities (Y. Fu).

Table of Contents

The Elastic Dielectric Response of Elastomers Filled with Liquid Inclusions: From Fundamentals to Governing Equations
Over the past decade, soft solids containing electro-and magneto-active liquid—as opposed to solid—inclusions have emerged as a new class of smart materials with promising novel electro- and magneto-mechanical properties. In this context, a recent contribution has put forth a continuum theory that describes the macroscopic elastic behavior of elastomers filled with liquid inclusions under quasistatic finite deformations from the bottom up, directly in terms of their microscopic behavior at the length scale of the inclusions. This chapter presents the generalization of that theory to the coupled realm of the elastic dielectric behavior of such an emerging class of filled elastomers when in addition to undergoing quasistatic finite deformations they are subjected to quasistatic electric fields. The chapter starts with the description of the underlying fundamentals in the continuum—id est, kinematics, conservation of mass, Maxwell’s equations, balance of momenta, and constitutive behavior of both the bulk (the solid elastomer and the liquid inclusions) and the solid/liquid interfaces—and ends with their combination to formulate the resulting governing equations.
Oscar Lopez-Pamies
Modelling of Homogeneous and Composite Non-linear Electro-Elastic Elastomers
We present in a concise way the main features of non-linear electro-elastic modelling of homogeneous and composite elastomers. We focus on some significant examples: three types of actuation of thin dielectric elastomers, search for bifurcations of prestretched membranes, introduction to modelling of two-phase laminates and optimization of performance of a dielectric energy generator that is assumed as a prototypical example of a soft dielectric device.
Massimiliano Gei
A Unified Theoretical Modeling Framework for Soft and Hard Magnetorheological Elastomers
These notes put together a number of theoretical and numerical models and results obtained for magnetically soft and hard magnetorheological elastomers, denoted as s-MREs and h-MREs, respectively over the last five years in our group. We present in a unified manner both s- and h-MREs. In particular, we regard MREs, in the general case, as magnetically dissipative nonlinear elastic composite materials comprising a mechanically-soft, non-magnetic elastomeric matrix in which mechanically-rigid, magnetically-dissipative particles are embedded isotropically and randomly. The proposed incremental variational frameworks are general enough to deal with more complex microstructures such as particle-chains or others that do not yet exist in the lab. More importantly, we propose homogenization-guided, analytical, explicit models that are consistent as one moves from the dissipative h-MREs to the purely energetic s-MREs. In parallel, we propose numerical frameworks allowing to simulate a very wide variety of microstructures and boundary value problems in magneto-mechanics.
Kostas Danas
Elastic Localizations
The past few decades have witnessed a surge of interest in pattern formations in soft materials under various fields. This has partly been driven by the recognition that buckling-induced patterns at micrometer and submicrometer scales may serve many useful purposes. Such patterns are usually either periodic or localized. Formation of periodic patterns is universally recognized as a bifurcation problem, and theories concerning periodic patterns have been well-developed and can be found in many textbooks and research monographs. In contrast, the initiation and evolution of localized patterns are rarely studied as a bifurcation problem, and when they are the discussion is often incomplete. In this chapter, we discuss three representative elastic localization problems: localized bulging of an inflated hyperelastic tube, localized necking of a solid cylinder induced by surface tension, and axisymmetric necking of a circular plate under all-round tension. All these problems are characterized by the fact that a linear bifurcation analysis would predict that the critical wavenumber is zero if the dimension in the direction of periodic variation is infinite. It is shown how the entire localization process, including initiation, growth and propagation, can be described analytically or semi-analytically, and how the process depends on how loading is carried out. It is also shown how a one-dimensional reduced model can be derived for the inflation problem and used to describe the entire localization process fairly accurately. It is hoped that the methodology explained here can be applied to study similar problems that also involve other effects such as electric and magnetic fields, chemical reactions, material deterioration, and residual stresses.
Yibin Fu
Electro- and Magneto-Mechanics of Soft Solids
Kostas Danas
Oscar Lopez-Pamies
Copyright Year
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