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Advanced Elasticity

computational nonlinear elasticity references

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I will be developing constitutive material models into commercial FE codes for nonlinear elasticity and searching for good books to get started for computational aspects. There are many good books for computational plasticity but I did not find any for nonlinear elasticity. Suggestion for good books or references is welcome.

Zhigang Suo's picture

Elastomer in equilibrium with forces and solvent

A long polymer consists of many monomers. The monomers are covalently bonded, and two bonded monomers may rotate relative to each other. Consequently, the polymer may be modeled as a chain of many links, each link representing a monomer. At a finite temperature, the polymer rapidly changes from one configuration to another.

A large number of long, flexible polymers can be crosslinked by covalent bonds to form a three-dimensional network. Subject to forces, the network undergoes large elastic deformation. The network is commonly called an elastomer.

Zhigang Suo's picture

Theory of dielectric elastomers

In response to a stimulus, a soft material deforms, and the deformation provides a function. We call such a material a soft active material (SAM). This review focuses on one class of soft active materials: dielectric elastomers. Subject to a voltage, a membrane of a dielectric elastomer reduces thickness and expands area, possibly straining over 100%. The phenomenon is being developed as transducers for broad applications, including soft robots, adaptive optics, Braille displays, and electric generators.

Tony Rockwell's picture

Addendum To Pressure and Chemical Potential - a question on hydrostatics

The question was raised in class as to what the appropriate equilibrium condition for a column of fluid at rest should be. Specifically, given we expect a hydrostatic gradient in pressure with height, whether  the chemical potential must be the same throughout the column was questioned. Here are my first thoughts. In brief, I assert that  the chemical potential must be everywhere identical, and that the pv term is balanced, at every height in the column, by the potential energy conferred by position in a gravitational field.

Cai Shengqiang's picture

Poroelasticity and diffusion in elastic solids

These are slides of poroelasticity and diffusion in elastic solids for final presentation based on ES241 notes.

Yuhang Hu's picture

advanced elasticity 2009 slides (polyelectrolyte gels)

These slides are based on an on-going paper written by Wei Hong, Xuanhe Zhao and Zhigang Suo and Suo's talk in ucsb.

Final presentation

Attached is my final presentation.

Final presentation slides

Here are the slides for my final presentation for ES 241.  During the presentation, a few suggestions were made, which I plan to follow up on.  Please check back here or subscribe for updates.

Tony Rockwell's picture

Slides on Pressure and Chemical Potential

Here are some slides I made on the subject of "Pressure and Chemical Potential" for the final meeting of Prof. Zhigang Suo's ES 241 class in the Spring of 2009.

Zhigang Suo's picture

A course on Advanced Elasticity, with emphasis on thermodynamics and soft active materials

In the field of Solid Mechanics, Harvard has a sequence of 5 graduate courses:

The first course goes over linear elasticity, finite element method, vibration, waves, viscoelasticity, as well as some ideas of finite deformation.

Zhigang Suo's picture

Finite Deformation: Special Cases

The notes on finite deformation have been divided into two parts: special cases and general theory (node/538). In class I start with special cases, and then sketch the general theory. But the two parts can be read in any order.

Zhigang Suo's picture

Free Energy

For a system in thermal contact with the rest of the world, we have described three quantities: entropy, energy, and temperature. We have also described the idea of a constraint internal to the system, and associated this constraint to an internal variable.

Need a book

Hi,

I am an engineer woking in structures at Whirlpool. I am looking for a

book Theory of Elasticity by Timoshenko and Goodier (Third Edition). If

anybody has a soft copy of it or a link to it, can you please send it to me via e-mail.

I'll highly appreciate your help.

Thanks in advance,

Harshal

Zhigang Suo's picture

ES 241 Advanced Elasticity Final Examination

Update on 23 May 2009:  I'm adding links to the slides as they are uploaded.

The final exam will take the form of a pedagogical workshop. We have 8 students taking the class for credit. I have divided the lecture notes into 8 parts as follows.

Henry Tan's picture

Instabilities in Material Behaviors

The linked two of my studies can be used as references for Zhigang’s lecture on Instabilities.

(1) Catastrophic fracture

Zhigang Suo's picture

Instabilities

  • Free energy and generalized coordinate. Equilibrium and stability
  • Control parameter
  • Configurational transitions of two types
  • Critical point of configurational transition of the second type. Bifurcation analysis
  • Behavior near a critical point. Post-bifurcation analysis
  • Load-displacement relation near a critical point
  • Koiter's theory of imperfection sensitivity
  • A family of systems of many degrees of freedom
  • Mode of bifurcation
  • Vibration in the neighborhood of an equilibrium configuration
Zhigang Suo's picture

Complex variable methods

  • What types of PDEs can be solved using complex variable methods
  • Anti-plane shear
  • Elements of a function of a complex variable (contour integral, analytic continuation, conformal mapping)
  • Line force
  • Screw dislocation
  • Crack
  • Circular hole
  • Elliptic hole
  • Plemelj formulas
  • Riemann-Hilbert problem
  • Crack interacting with a point singularity
  • In-plane deformation
  • Dundurs parameters
  • Interfacial cracks
  • Anisotropic materials. Stroh formalism
Zhigang Suo's picture

Homework on finite deformation

To the students of ES 241:

Although finite deformation was introduced in ES 240 (Solid Mechanics), finite deformation is a building block of ES 241. To review the subject, please go over a set of problems compiled by Jim Rice. If you need a reference, see my outline of finite deformation, where you can also find a short list of textbooks.

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