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Biswajit Banerjee's blog

Derivative of Logarithmic Strain

Some of you probably work on problems that involve moderately large strains. An useful strain measure for such problems in the logarithmic or Hencky strain. In particular, if you deal with the numerics of large strain simulations, you will often need to compute the material time derivatives of logarithmic strains.

On digitizing and editing figures

Recently I have observed that if I don't perform a routine task for a few months, I tend to forget the steps needed in the process. I have to relearn the process and that's a waste of time. The intention of this blog post is to provide a list of tips for my use which can also be of use to other Linux users. I like free software. Most of the software on this list can be downloaded from SourceForge or some such place.


Graeme Milton to be awarded the 2007 Prager Medal

Professor Graeme Milton will be awarded the 2007 Prager medal from the Society of Engineering Science for his work on solid mechanics.  The medal will be handed out at the 44th Annual Technical Meeting of the Society of Engineering Science (SES2007) to be held between October 21 and 24, 2007 at College Station, Texas.

An interesting coupling

A video that shows how some common couplings work. It's an advertisement but interesting nevertheless.  Does anyone know how the Thomson coupling works and what its main drawbacks are? It seems a bit complex and will probably have a higher rate of failure than simpler geometries - but maybe not?

Mechanical Threshold Stress model for 6061-T6 aluminum alloy

I have attached a copy of my McMat07 talk below.  The talk is about a modified mechanical threshold stress (Follansbee-Kocks) model that can be used for strain rates > 1000 /s and high homologous temperatures.  In the model, the pressure dependence of the flow stress arises from the pressure dependence of the shear modulus.  Even after using the most accurate models for the shear modulus (and the melting temperature) we find that the pressure sensitivity of the flow stress is underestimated by our model (by quite a bit).

Peridynamic theory vs. classical continuum theory

Dr. Stewart Silling has provided me with a copy of his talk on Peridynamic theory that he presented at McMat 2007.  The PDF file of the talk is attached below.

In order to deal with classical material models and volume constraints, Dr. Silling has modified the original theory to allow for forces that are not necessarily pairwise. A bit on that is included in the talk.

Dynamic Behavior and Failure of Materials - McMat07

The schedule for the McMat07 session on dynamic behavior and failure is given below.  My talk will be an a flow stress model for high strain rates and high temperatures applied to 6061-T6 aluminum alloy.  Hope to see youin Austin.


7-2 Dynamic Behavior and Failure of Materials

Topic Chair: Tracy Vogler, Sandia National Laboratories

Topic Co-Chair: Rebecca Brannon, University of Utah

7-2-1 Dynamic Response of Materials 1
(Technical Session)

Derivatives of the invariants of a tensor

When you first start learning finite deformation plasticity, you will run into a plastic flow rate $ \ensuremath{\boldsymbol{d}}_p$ that can be derived from a flow potential $ \phi$ such that 

Method of Manufactured Solutions

Nowadays, we often use the tools of computational analysis in engineering design. For the results of such analyses to be believable, the tools that are used have to pass rigorous tests. There are two categories of tests involved:

Simulating explosions

Recently Henry talked about software that could be used to simulate explosions and introduced CartaBlanca. Luming asked whether anyone had used the software, how good it was, and whether one needed Java to implement models into CartaBlanca.

Some weekend reading

Terence Tao (one of the Fields Medal winners this year) has started blogging. He has a detailed discussion on the Navier-Stokes equations here. It's long but definitely worth reading - particularly because of the wide range of ideas that he talks about.

Which phenomenological flow stress model is the best?

A couple of years ago a colleague who wanted to simulate high-speed machining asked me: " Which is the best phenomenological flow stress model for metals?" I wasn't able to give an answer right away and decided to look in the literature.

What I found was, every ten years or so, a new model appears in the literature that tries to solve some of the problems of older models. However, a clear ranking of models has not been established yet.

Is there a shear instability in metal foams?

Last year I spent three months modeling the compressive behavior of aluminum alloy foams. I had hoped to find some evidence of the banding instability that is often observed in elastomeric foams [1]. Lakes writes that this sort of banding instability provides indirect experimental evidence for negative shear modulus [2].


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