Amit Acharya's blog

In the post

 node/9509

(Journal of Elasticity, Carlson memorial Volume)

A methodology is devised to utilize the statistical mechanical entropy of an isolated, constrained atomistic system to define the dissipative driving-force and energetic fields in continuum thermomechanics. A thermodynamic model of dislocation mechanics is discussed. One outcome is a definition for the mesoscale back-stress tensor and the symmetric, polar dislocation density-dependent, Cauchy stress tensor from atomistic ingredients.

It is with great sadness that I report the passing away of Prof. Don Carlson. The link below describes his life and work.

http://mechse.illinois.edu/content/news/article.php?article_id=410

Amit Acharya and Kaushik Dayal

 (To appear in Quarterly of Applied Mathematics)

This paper presents a generalization of traditional continuum approaches to liquid crystals and

liquid crystal elastomers to allow for dynamically evolving line defect distributions. In analogy with

recent mesoscale models of dislocations, we introduce fields that represent defects in orientational

and positional order through the incompatibility of the director and deformation ‘gradient’ fields.

 (in Computational Methods for Microstructure-Property Relationships," Springer. Edited by Somnath Ghosh and Dennis Dimiduk)

Dislocation mediated continuum plasticity: case studies on modeling scale dependence, scale-invariance, and directionality of sharp yield-point

Claude Fressengeas, Amit Acharya, Armand Beaudoin

(in Journal of the Mechanics and Physics of Solids)

Johannes Zimmer, Karsten Matthies, Amit Acharya

(in Journal of the Mechanics and Physics of Solids)

This post is in response to the imechanica request

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 (a separate post, as I have to attach notes - it would be really nice to be able to attach documents to imechanica comments)

 Attached are hand-written notes I have used to implement the Network B for the Bergstrom-Boyce model. They were written for my use only, so if it seems stream-of-consciousness at times, don't blame me. The details should all be there, though.

I post some (hand-written) notes on compatibility conditions for both small and finite strains that I have used for helping me in lecturing. These may be useful for our student friends on imechanica. I also post a paper on compatibility conditions for the Left Cauchy-Green field in three dimensions as well as the paper by Janet Blume on the same subject.

 in B. D. Reddy (ed.). IUTAM Symposium on Theoretical, Modelling, and Computational Aspects of Inelastic Media, 99-105. Springer Science, 2008.