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Zhigang Suo's picture

Mechanics of Soft Active Materials

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.

Zhigang Suo's picture

Elastic dielectrics, slides for a short tutorial

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:

Zhigang Suo's picture

Large deformation and instability in gels

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:

Xuanhe Zhao's picture

Inhomogeneous and anisotropic equilibrium state of a swollen hydrogel containing a hard core

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.

Wei Hong's picture

Drying-induced bifurcation in a hydrogel-actuated nanostructure

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.

Zhigang Suo's picture

Electromechanical instability of large deformation in dielectric elastomers

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.

Nanshu Lu's picture

Co-evolution of local thinning and debonding

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.

Wei Hong's picture

A theory of coupled diffusion and large deformation in polymeric gels

   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.

Xuanhe Zhao's picture

Stretching and polarizing a dielectric gel immersed in a solvent

      This paper studies a gel formed by a network of cross-linked polymers and a species of mobile molecules. The gel is taken to be a dielectric, in which both the polymers and the mobile molecules are nonionic. We formulate a theory of the gel in contact with a solvent made of the mobile molecules, and subject to electromechanical loads. A free-energy function is constructed for an ideal dielectric gel, including contributions from stretching the network, mixing the polymers and the small molecules, and polarizing the gel.

Xuanhe Zhao's picture

A method to analyze electromechanical stability of dielectric elastomer actuators

      This letter describes a method to analyze electromechanical stability of dielectric elastomer actuators.  We write the free energy of an actuator using stretches and nominal electric displacement as generalized coordinates, and pre-stresses and voltage as control parameters.  When the Hessian of the free-energy function ceases to be positive-definite, the actuator thins down drastically, often resulting in electrical breakdown.  Our calculation shows that stability of the actuator is markedly enhanced by pre-stresses.

Jinxiong Zhou's picture

Propagation of instability in dielectric elastomers

When an electric voltage is applied across the thickness of a thin layer of an dielectric elastomer, the layer reduces its thickness and expands its area. This electrically induced deformation can be rapid and large, and is potentially useful as soft actuators in diverse technologies. Recent experimental and theoretical studies have shown that, when the voltage exceeds some critical value, the homogenous deformation of the layer becomes unstable, and the layer deforms into a mixture of thin and thick regions.

Chip-package interaction and interfacial delamination

In flip-chip package, the mismatch of thermal expansion coefficients between the silicon die and packaging substrate induces concentrated stress field around the edges and corners of silicon die during assembly, testing and services. The concentrated stresses result in delamination on many interfaces on several levels of structures, in various length scales from tens of nanometers to hundreds of micrometers. A major challenge to model flip-chip packages is the huge variation of length scales, the complexity of microstructures, and diverse materials properties. In this paper, we simplify the structure to be silicon/substrate with wedge configuration, and neglect the small local features of integrated circuits. This macroscopic analysis on package level is generic with whatever small local features, as long as the physical processes of interest occur in the region where the concentrated stress field due to chip-packaging interaction dominates. Because it is the same driving force that motivates all of the flaws. Therefore, the different interface cracks with same size and same orientation but on different interfaces should have similar energy release rates provided that the cracks are much smaller than the macroscopic length. We calculate the energy release rate and the mode angle of crack on the chip-package interface based on the asymptotic linear elastic stress field. In a large range of crack length, the asymptotic solution agrees with finite element calculation very well. We discuss the simplified model and results in context of real applications. In addition, we find that the relation of energy release rate G and crack length a is not power-law since local mode mixity is dependent of crack length a. Therefore, the curve of G~a can be wavy and hardly goes to zero even if crack length a goes to atomically small. The local mode mixity plays an important role in crack behavior.

Xuanhe Zhao's picture

Electromechanical hysteresis and coexistent states in dielectric elastomers

Active polymers are being developed to mimic a salient feature of life: movement in response to stimuli. Large deformation can lead to intriguing phenomena; for example, recent experiments have shown that a voltage can deform a layer of a dielectric elastomer into two coexistent states, one being flat and the other wrinkled. This observation, as well as the needs to analyze large deformation under diverse stimuli, has led us to reexamine the theory of electromechanics.

Nanshu Lu's picture

Delamination of stiff islands patterned on stretchable substrates

As another celebration of March Journal Club of Mechanics of Flexible Electronics, this paper has just been submitted.


In one design of flexible electronics, thin-film islands of a stiff material are fabricated on a polymeric substrate, and functional materials are grown on these islands. When the substrate is stretched, the deformation is mainly accommodated by the substrate, and the islands and functional materials experience relatively small strains. Experiments have shown that, however, for a given amount of stretch, the islands exceeding a certain size may delaminate from the substrate. We calculate the energy release rate using a combination of finite element method and complex variable method. Our results show that the energy release rate diminishes as the island size or substrate stiffness decreases. Consequently, the critical island size is large when the substrate is compliant. We also obtain an analytical expression for the energy release rate of debonding islands from a very compliant substrate.

Martijn Feron's picture

Split singularities and dislocation injection in strained silicon

By Martijn Feron, Zhen Zhang and Zhigang Suo

The mobility of charge carriers in silicon can be significantly increased when silicon is subject to a field of strain.In a microelectronic device, however, the strain field may be intensified at a sharp feature, such as an edge or a corner, injecting dislocations into silicon and ultimately failing the device. The strain field at an edge is singular, and is often a linear superposition of two modes of different exponents. We characterize the relative contribution of the two modes by a mode angle, and determine the critical slip systems as the amplitude of the load increases. We calculate the critical residual stress in a thin-film stripe bonded on a silicon substrate.

Zhigang Suo's picture

A field of material particles vs. a field of markers

In continuum mechanics, it is a common practice to view a body as a field of material particles, so that the continuum mechanics is phrased as an algorithm to determine the function x(X, t), where X is the name of a particle, and x is the place of the particle at time t.

Nicolas Cordero's picture

Channel cracks in a hermetic coating consisting of organic and inorganic layers

Abstract: Flexible electronic devices often require hermetic coatings that can withstand applied strains. This paper calculates the critical strains for various configurations of channel cracks in a coating consisting of organic and inorganic layers. We show that the coating can sustain the largest strain when the organic layer is of some intermediate thicknesses.

Flexible electronics are promising for diverse applications, such as rollable displays, conformal sensors, and printable solar cells. These systems are thin, rugged, and lightweight. They can be manufactured at low costs, for example, by roll-to-roll printing. The development of flexible electronics has raised many issues concerning the mechanical behavior of materials. This paper examines a particular issue: channel cracks in hermetic coatings.

Electronic devices (e.g., organic light-emitting devices, OLEDs) often degrade when exposed to air. Developing hermetic coatings has been a significant challenge. Organic films are permeable to gases, and inorganic films inevitably contain processing flaws, so that neither by themselves are effective gas barriers. These considerations have led to the development of multilayer coatings consisting of alternating organic and inorganic films. To be used in flexible electronics, these coatings must also withstand applied strains without forming channel cracks...

Teng Li's picture

Delocalizing Strain in a Thin Metal Film on a Polymer Substrate

Teng Li, Zhenyu Huang, Zhichen Xi, Stephanie P. Lacour, Sigurd Wagner, Zhigang Suo, Mechanics of Materials, 37, 261-273 (2005).

Under tension, a freestanding thin metal film usually ruptures at a smaller strain than its bulk counterpart. Often this apparent brittleness does not result from cleavage, but from strain localization, such as necking. By volume conservation, necking causes local elongation. This elongation is much smaller than the film length, and adds little to the overall strain. The film ruptures when the overall strain just exceeds the necking initiation strain, εN , which for a weakly hardening film is not far beyond its elastic limit. Now consider a weakly hardening metal film on a steeply hardening polymer substrate. If the metal film is fully bonded to the polymer substrate, the substrate suppresses large local elongation in the film, so that the metal film may deform uniformly far beyond εN. If the metal film debonds from the substrate, however, the film becomes freestanding and ruptures at a smaller strain than the fully bonded film; the polymer substrate remains intact. We study strain delocalization in the metal film on the polymer substrate by analyzing incipient and large-amplitude nonuniform deformation, as well as debond-assisted necking. The theoretical considerations call for further experiments to clarify the rupture behavior of the metal-on-polymer laminates.

Related posts and discussions

Tension of Cu film on Pi substrate
Local thinning of Cu film
High ductility of a metal film adherent on a polymer substrate


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