Amit Acharya's blog

(This paper is to appear in the IUTAM Procedia on "Linking scales  in computations: from microstructure to macro-scale properties," edited by Oana Cazacu)

Amit Acharya, S. Jonathan Chapman

(to appear in International Journal of Fracture; Proceedings of the 5th Intl. Symposium on Defect andMaterial Mechanics)

Amit Acharya and Claude Fressengeas

(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.

 
(to appear in the Intl. Journal of Engineering Science)

 Robin J. Knops and Amit Acharya

 The relationship between dislocation theory and the difference of linear elastic solutions for two different sets of elastic moduli, derived by Filon in two-dimensions, is generalised to three-dimensions. Essential features are developed and illustrated by the  examples of the edge and screw dislocations. The inhomogeneity  problem is  discussed within the same context and related to Somigliana dislocations, and  in the limit  to the interstitial atom.

Luc Tartar and Amit Acharya

Bulletin of the Italian Mathematical Union, (9)IV, 409-444, 2011

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

node/5034

 (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.

The main idea is the following: a most natural mathematical setup for considering the motion of the void-solid interface of an expanding void is that of the traveling wave. Thus, a theory for macroscopic damage evolution may be suspected as being a homogenized version of basic theory that has such wave phenomena as an essential ingredient. This paper is a first step in probing such questions. 

I came across some content I used to have on my webpage a long time ago.

http://www.ce.cmu.edu/~amita/webpage_misc.html

Hopefully it is inspirational for that bright, young, graduate student waiting in the wings to usher in the revolution that shows us how to solve some of the outstanding theoretical problems of solid mechanics that we seem to put off  e.g. concrete, quantitative methods for calculating time-dependent microstructure in plasticity and its effect on time-dependent macroscopic properties.....

A technique for setting up generalized continuum theories based on a balance law and nonlocal thermodynamics is suggested. The methodology does not require the introduction of gradients of the internal variable in the free energy. Elements of a generalized damage model with porosity as the internal variable are developed as an example.

A field theory of dislocation mechanics and plasticity is illustrated through new results at the nano, meso, and macro scales. Specifically, dislocation nucleation, the occurrence of wave-type response in quasi-static plasticity, and a jump condition at material interfaces and its implications for analysis of deformation localization are discussed.

 The Koiter-Sanders-Budiansky bending strain measure and a nonlinear generalization

 We know from strength of materials that non-uniform stretching of fibers along the cross section of a beam produces bending moments. But does this situation necessarily correspond to a 'bending' deformation? For that matter, what do we exactly mean kinematically when we talk about a bending deformation?

Attached is a paper outlining ideas for averaging autonomous dynamics, based on a dynamical systems point of view.

People interested in computational multiscale modeling, especially of the sequential kind, as well as nonequilibrium statistical mechanics may find these ideas useful.