For a flexible electronic device integrating inorganic materials on a polymer substrate, the polymer can deform substantially, but the inorganic materials usually fracture at small strains.  This paper describes an approach to make such a device highly stretchable.  A polyimide substrate is first coated with a thin layer of an elastomer, on top of which SiNx islands are fabricated.  When the substrate is stretched to a large strain, the SiNx islands remain intact.  Calculations confirm that the elastomer reduces the strain in the SiNx islands by orders of magnitude.

In a lithium-ion battery, both electrodes are atomic frameworks that host mobile lithium ions. When the battery is being charged or discharged, lithium ions diffuse from one electrode to the other. Such an insertion reaction deforms the electrodes, and may cause the electrodes to crack. This paper uses fracture mechanics to determine the critical conditions to avert cracking. The method is applied to cracks induced by the mismatch between phases in crystalline particles of LiFePO4

Electromechanical instability in semicrystalline polymers
Xuanhe Zhao , Zhigang Suo
Abstract
When a layer of a semicrystalline polymer is subject to a tensile force in its plane and a voltage through its thickness, the deformation of the layer is initially homogeneous,but then localizes.

This paper studies the dynamic behavior of a dielectric elastomer balloon subject to a combination of pressure and voltage.  When the pressure and voltage are static, the balloon may reach a state of equilibrium.  We determine the stability of the state of equilibrium, and calculate the natural frequency of the small-amplitude oscillation around the state of equilibrium.  When the voltage is sinusoidal, the balloon resonates at multiple frequencies of excitation, giving rise to superharmonic, harmonic, and subharmonic responses.  When the frequency of excitation varies continuously, the oscillating amplitude of the balloon may jump, exhibiting hyste

Mechanical energy can be converted to electrical energy by using a dielectric elastomer generator.  The elastomer is susceptible to various modes of failure, including electrical breakdown, electromechanical instability, loss of tension, and rupture by stretch.  The modes of failure define a cycle of maximal energy that can be converted.  This cycle is represented on planes of work-conjugate coordinates, and may be used to guide the design of practical cycles.

An electronic device integrates diverse materials, and inevitably contains sharp features, such as interfaces and corners. When the device is subject to thermal and mechanical loads, the corners develop intense stress and are vulnerable sites to initiate failure. This paper analyzes stress fields at corners in flip-chip packages. The stress at a corner is a linear superposition of two modes of singular fields, with one mode being more singular than the other. The amplitudes of the two modes are represented by two stress intensity factors of dissimilar dimensions. To determine the stress intensity factors, we analyze the flip-chip structures under two loading conditions: stretching of the substrate and bending of the substrate.

As a complement to the current issue of journal club, I would like to bring your attention to our current work on dielectric elastomers. 

Xuanhe Zhao and Zhigang Suo A layer of a dielectric elastomer expands its area when a voltage is applied across its thickness.  The layer can be programmed to deform in three dimensions by using patterned prestretches, electrodes, and stiffeners. 

Dielectric elastomers are capable of large deformation subject to an electric voltage, and are promising for uses as actuators, sensors and generators. Because of large deformation, nonlinear equations of state, and diverse modes of failure, modeling the process of electromechanical transduction has been challenging.  This paper studies a membrane of a dielectric elastomer deformed into an out-of-plane, axisymmetric shape, a configuration used in a family of commercial devices known as the Universal Muscle Actuators. 

A gel is an aggregate of polymers and solvent molecules.  The polymers crosslink into a three-dimensional network by strong chemical bonds, and enable the gel to retain its shape after a large deformation.  The solvent molecules, however, interact among themselves and with the network by weak physical bonds, and enable the gel to be a conduit of mass transport.  The time-dependent concurrent process of large deformation and mass transport is studied by developing a finite element method. 

Xuanhe Zhao and Zhigang Suo  We develop a thermodynamic model of electrostriction for elastic dielectrics capable of large deformation. The model reproduces the classical equations of state for dielectrics at small deformation, but shows that some electrostrictive effects negligible at small deformation may become pronounced at large deformation.

Subject to a voltage, a dielectric elastomer can deform substantially, making it a desirable material for actuators. Designing such an actuator, however, has been challenging due to nonlinear equations of state, as well as multiple modes of failure, parameters of design, and measures of performance. This paper explores these issues, using a spring-roll actuator as an example. We formulate the equations of state of two degrees of freedom, and describe the constraints due to several modes of failure of the elastomer, including electrical breakdown, electromechanical instability, loss of tension, and tensile rupture. Also included is the compressive limit of the spring.

In a previous paper , we have demonstrated that a microcrystalline copper film well bonded to a polymer substrate can be stretched beyond 50% without cracking. The film eventually fails through the co-evolution of necking and debonding from the substrate. Here we report much lower strains to failure (around 10%) for polymer-supported nanocrystalline metal films, whose microstructure is revealed to be unstable under mechanical loading.

At the invitation of David Clarke on behalf of the UCSB/Los Alamos Institute of Multiscale Materials and Structures, I gave the following three lectures:

1. Large deformation and instability in dielectric elastomers
2. Large deformation and instability in swelling polymeric gels
3. Mechanics and electrochemistry of polyelectrolyte gels

The abstracts follow, and the slides are attached at the end of this post.

A network of polymers can imbibe a large quantity of a solvent and swell, resulting in a gel.  The swelling process can be markedly influenced by a mechanical load and geometric constraint.  When the network, solvent, and mechanical load equilibrate, the gel usually swells by a field of inhomogeneous and anisotropic deformation.  We show that this field in the swollen gel is equivalent to that in a hyperelastic solid.  We implement this theory in the finite-element package, ABAQUS, and analyze examples of swelling-induced deformation, contact, and bifurcation.  Because commercial software like ABAQUS is widely available, this work may provide a powerful tool to study complex phenomena in gels.

Rob Wood teaches a course on micro/nano robotics, and asks me to give a 30-minute tutorial on the theory of dielectric elastomer actuators (DEAs).  I attach my slides, which might be useful to you if you'd like to include this topic in your class.  The tutorial draws upon work in the literature, as well as recent work in my group:

I'm attaching slides of a talk that I gave yesterday at the Schlumberger-Doll Research Center.  In preparing the talk, I made liberal use of slides prepared by Wei Hong for his own presentations.  The talk is mainly based on the following papers:

A polymer network can imbibe water from environment and swell to an equilibrium state. If the equilibrium is reached when the network is subject to external mechanical constraint, the deformation of the network is typically anisotropic, and the concentration of water inhomogeneous.  Such an equilibrium state in a network constrained by a hard core is modeled here with a nonlinear differential equation.  The presence of the hard core markedly reduces the concentration of water near the interface and causes high stresses.

Hydrogels have enormous potential for making adaptive structures in response to diverse stimuli.  In a structure demonstrated recently, for example, nanoscale rods of silicon were embedded vertically in a swollen hydrogel, and the rods tilted by a large angle in response to a drying environment (Sidorenko, et al., Science 315, 487, 2007).  Here we describe a model to show that this behavior corresponds to a bifurcation at a critical humidity, analogous to a phase transition of the second kind.

I attach slides for an ASME talk, which is based on a recent paper.

I attach the slides of a presentation at the ASME meeting.  The talk was based on several recent papers on soft active materials (SAMs).  To give an uncluttered picture of the pull-in instability, I have removed all discussion on the Maxwell stress.   As you can see, the problem can be studied without ever mentioning this troublesome notion.

I have recently given seminars on Mechanics of Soft Active Materials (SAMs) at several universities, using this set of slides (pdf, 1.4 MB).  I also attach the slides as ppt; please feel free to use anyway you want.  Here is an abstract of the seminars, followed by a list of papers published by my group on the topic.  Each paper has initiated on iMechanica a thread of discussion, to which I'll link.  I'll give a talk at the ASME Congress in Seattle, in Session 10-12-4 Instability in Solids, 9:45 am - 11:15 am, Thursday, 15 November 2007.  

A 1um-thick Cu film was deposited on Kapton 50HN substrate, with a thin Cr interlayer to improve adhesion. The specimen was in-situ annealed at 200oC for 30min after deposition.

This FIB image was taken after the specimen was uniaxially stretched to 50% and released.

A link for the paper: http://www.seas.harvard.edu/suo/papers/201.pdf

   A large quantity of small molecules may migrate into a network of long polymers, causing the network to swell, forming an aggregate known as a polymeric gel.  This paper formulates a theory of the coupled mass transport and large deformation.