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Time-averaged coarse variables for multiscale dynamics

Submitted by Amit Acharya on
research
multiscale modeling
singular perturbations
time-averaging

(to appear in Quarterly of Applied Mathematics)

by Marshall Slemrod and Amit Acharya

Given an autonomous system of Ordinary Diff erential Equations without an a priori split into slow and fast components, we defi ne a strategy for producing a large class of `slow' variables (constants of fast motion) in a precise sense. The equation of evolution of any such slow variable is deduced. The strategy is to rewrite our system on an in finite dimensional "history" Hilbert space X and defi ne our coarse observation as a functional on X.

Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels

Submitted by Cai Shengqiang on
research
suo group research
hydrogels
phase transition
temperature-sensitive

This paper uses the thermodynamic data of aqueous solutions of uncrosslinked poly(N-isopropylacrylamide) (PNIPAM) to study the phase transition of PNIPAM hydrogels.  At a low temperature, uncrosslinked PNIPAM  can be dissolved in water and form a homogenous liquid  solution.  When the temperature is increased, the solution separates into two liquid phases with different concentrations of the polymer.   Covalently crosslinked PNIPAM, however, does not dissolve in water, but can imbibe water and form a hydrogel.  When the temperature is changed

See while you Measure: In-situ Studies in Mechanics (September Journal Club Topic)

Submitted by Aman Haque on
research
mechanics
in-situ electron microscopy

*Participation to this club is as easy as i) sending a reference/abstract of your paper if you are working in this area or ii) send a challenge concept/issue/expt if you are not experimentalist :)*  

Problem of Model Verification for a Curved Beam Model

Submitted by Jia-Jie Guo on
research
FEA
curved beam
model verification

Dear all,

I have a problem in model verification for a curved beam model. I have formulated an Euler-Bernoulli beam model similar to the following paper (refered as Pai's model), but employing Euler angle description.

         Pai,
P.F., Palazotto, A.N., 1996, “Large-deformation analysis of flexible beams,” International Journal of Solids Structures,
33(9), pp. 1335-1353.

Calculate height of hydraulic fracture

Submitted by Kan Wu on
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I need to calculate the height of hydraulic fracture using P3D and the width in the vertical direction. The width in the lateral direction is computed by displacement discontinuity method. These two widthes are totally different calculated by my coding. Please give me some advice. 

crack propagation in thin films

Submitted by bronger on
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Fracture Mechanics Forum
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I work in a thin-film photovoltaics institute.  We deposit 1 µm silicon on glass substrate.  This silicon has tensile stress.

Then, by etching through a tiny hole in the silicon with HF, we underetch the thin layer.  This way, a circular area of the silicon is unattached to the glass.  The circle grows with time. We observe spirals of cracks at these positions.  Sometimes, there's only one spiral, sometimes we see two nested spirals.

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