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.

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.

      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. We show that the free-energy function is non-convex, leading to instabilities. We also show that mechanical constraint markedly affects the behavior of the gel.

      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.

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. In his classic text, Maxwell showed that electric forces between conductors in a vacuum could be calculated using a field of stress in the vacuum. The Maxwell stress has since been invoked in deformable dielectrics. This practice has been on an insecure theoretical foundation.

I'm Xuanhe Zhao, a first year PhD student working in Suo's Group, at Harvard University. Prior to coming to Harvard, I obtained a Master Degree in Materials Engineering from University of British Columbia.

The mechanical performance of a homogeneous material can be varied by the addition of second-phase particles. In this project, we will model a planar composite under plastic deformation. As shown on the following figure, the composite consists of matrix material and randomly-distributed inclusion particles. The matrix is assumed to be an elastic-plastic material with isotropic or kinematic hardenings, and the inclusion particle pure elastic with a higher Young’s modulus. The stress/strain field throughout the composite will be calculated numerically with finite element method. The effective constitutive behavior of the composite will be evaluated and compared with theoretical and experimental results from literature [1, 2].

Measuring mechanical properties of materials on a very small scale is a difficult, but increasingly important task. There are only a few existing technologies for conducting quantitative measurements of mechanical properties of nanostructures, and nano-indentation is the leading candidate. In this project, we simulate the nano-indentation tests of thin film materials using finite element software ABAQUS. The materials properties and test parameters will be taken from references on nano-indentation experiments [1, 2]. Therefore, the model can be validated by comparing its predictions with experiment results. In addition, we will change 1) the thickness of the thin film and 2) the material of the substrate (for the thin film) in the model, in order to study substrate's effects on nano-indentation tests.

I would like to recommend "Elasticity: Theory, Applications, and Numerics" by Prof. Martin H. Sadd as a reference for ES240. The book, as its name indicated, is mainly focused on elasticity theory and its applications, but also discusses numerical methods such as finite element method and boundary element method.

Prof. Martin H. Sadd, organized the book into two parts: I. foundations, and II Advanced topics. In part I, the book clearly outlines the basic equations of elasticity, i.e. strain/displacement relation, Hooke's law, and equilibrium equation. The other context of part I is devoted to the formulation and solution of two-dimensional problems. This structure matches the progress of our class very well.

The second part of the book begins with the discussion of anisotropic elasticity, thermo-elasticity, and micromechanics. These topics are complementary to the notes of ES240, and helpful in solving homework problems. In its last chapter, the book introduced finite element method and boundary element method.

My name is Xuanhe Zhao, and I'm a first year student in DEAS. Before joining Harvard, I got my Master Degree in Materials Engineering from University of British Columbia, Canand. I have took one course on Computational Mechanics, and read a couple of books on theory of elasticity.

 The major goal for me taking ES 240 is to learn how to understand and solve engineering problems, both familiar and unfamiliar, in a intuitive way. In addition, I will further consolidate my background in solid mechanics.

 University of Michigan, tenure-track faculty positions

The Department of Mechanical Engineering, University of Michigan, Ann Arbor, invites applications for tenure-track faculty positions in various areas of mechanical engineering including design and manufacturing, dynamics, systems and controls, materials and solid mechanics and thermal/fluid sciences. Candidates with research interests in automotive engineering, biotechnology, eco/sustainable systems, energy-systems, manufacturing, and micro/nano systems are particularly encouraged to apply.

Applicants should have an earned Ph.D. in Mechanical Engineering or related fields, a demonstrated record for conducting independent research, and the potential for leadership and impact in teaching and research. Appointments at all levels will be considered. For best consideration, candidates should apply by February 28, 2007, but the positions will remain open until filled.