Electro- and Magneto-Mechanics of Soft Solids: Constitutive Modelling, Numerical Implementations, and Instabilities (CISM International Centre for Mechanical Sciences, 610)

✍ Scribed by Kostas Danas (editor), Oscar Lopez-Pamies (editor)

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 185
• Category: Library

✦ Synopsis

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 andartificial 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

Preface
Contents
The Elastic Dielectric Response of Elastomers Filled with Liquid Inclusions: From Fundamentals to Governing Equations
1 Introduction
2 Initial Configuration and Kinematics
3 Conservation of Mass
4 Maxwell's Equations in the Presence of Material Interfaces
4.1 Bulk and Interface Charges, Electric Fields, and Electric Displacements
4.2 Gauss's Law
4.3 Faraday's Law
5 Balance of Momenta in the Presence of Material Interfaces
5.1 Bulk and Interface Electric and Mechanical Forces
5.2 Balance of Linear Momentum
5.3 Balance of Angular Momentum
6 Constitutive Behavior
6.1 Constitutive Behavior of the Bulk: The Solid Matrix and the Liquid Inclusions
6.2 Constitutive Behavior of the Solid/liquid Interfaces
7 Governing Equations
7.1 Boundary Conditions
7.2 The Choice of Independent Fields
7.3 The Strong Form of the Governing Equations
7.4 Residual Stresses
References
Modelling of Homogeneous and Composite Non-linear Electro-Elastic Elastomers
1 Introduction
2 Modelling of Electro-Elastic Materials
2.1 Electro-Elastic Constitutive Equations
2.2 Finite Electro-Elastic Actuation of Thin Films
3 Linearized Incremental Deformations
4 Global Bifurcations of Soft Dielectric Elastomers
4.1 Electro-Mechanical Instability
4.2 Diffuse-Mode Instabilities
5 Electro-Mechanics of Laminated Composites Under Plane-Strain Conditions
5.1 Constitutive Assumptions
5.2 Homogenized Solution Controlling the Voltage and Boundary Conditions
5.3 Macroscopic Performance
6 Introduction to Mechanical-to-Electrical Energy Conversion
6.1 Model of a DE Generator
6.2 The Load-Driven Harvesting Cycle and the Area of Admissible Configurations
6.3 Optimization of the Harvesting Cycle
7 Conclusions
References
A Unified Theoretical Modeling Framework for Soft and Hard Magnetorheological Elastomers
1 Introduction
2 Preliminary Definitions in Magneto-Elasto-Statics
2.1 Finite Strain Kinematics
2.2 Magnetostatics
3 Thermodynamics and General Variational Formulations
3.1 Scalar Potential-Based F-H Formulation
3.2 Vector Potential-Based F-B Formulation
4 Modeling of Isotropic Hard-MREs
4.1 Internal Variable for Magnetic Dissipation
4.2 General Properties of the Free Energy Density and the Dissipation Potential
4.3 The Isotropic Magneto-Mechanical Invariantspg for hh-MREs
4.4 Form of Energy Densities
4.5 The Mechanical Energy Density
4.6 The Magnetic and Coupled Energy Densities
4.7 The Dissipation Potential
4.8 Total Cauchy Stress in hh-MREs
5 Modeling of Isotropic Soft-MREs
5.1 F-H Expressions for ss-MREs
5.2 F-B Expressions for ss-MREs
5.3 Total Cauchy Stress in ss-MREs
6 Numerical Implementations for MREs
6.1 Time Discrete Variational Principle for F-H Formulation
6.2 Time Discrete Variational Principle for F-B Formulation
6.3 The Periodic Numerical Homogenization Problem
7 Results: Periodic RVE Simulations and Model Assessment
7.1 hh-MRE Models Versus FE Simulations
7.2 Magnetization Independent of Stretching in MREs
7.3 NdFeB-Based hh-MRE Versus CIP-Based ss-MRE Response
7.4 Energetic ss-MRE Models Versus hh-MRE Models with Zero Dissipation
8 Results: Numerical BVP Simulations
8.1 Generic Numerical BVP Setting
8.2 Treatment of Air
8.3 Magnetostriction and Magnetization Response of a Spherical ss-MRE Specimen
8.4 Uniformly Pre-magnetized hh-MRE Cantilever Beams
8.5 Non-uniformly Pre-magnetized, Functionally-Graded hh-MRE Cantilever Beams
References
Elastic Localizations
1 An Example of Bifurcation at Zero Wavenumber
2 Localized Bulging of an Inflated Hyperelastic Tube
2.1 Bifurcation Condition and Near-Critical Behaviour
2.2 Graphical Illustration of the Bifurcation Condition
2.3 Bulge Evolution—Fully Nonlinear Analysis
2.4 A 1D Gradient Model Under the Membrane Assumption
2.5 Evaluation of the Infinite Length Assumption
2.6 Tubes of Finite Wall Thickness
3 Necking of a Solid Cylinder Under Surface Tension
4 Axisymmetric Necking in a Circular Hyperelastic Plate Under Equibiaxial Stretching
4.1 Governing Equations and the Primary Solution
4.2 Linear Analysis
4.3 Weakly Nonlinear Analysis
4.4 Fully Nonlinear Regime
5 Conclusion
References