Attached are some (hand-written) observations on wanting to do continuum mechanics when mass is not conserved for fixed sets of particles of the body (so, situations transcending the rocket-losing-mass type). I feel (un)comfortable with these observations, depending upon the day I think about such things.
(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
Luc Tartar and Amit Acharya
Bulletin of the Italian Mathematical Union, (9)IV, 409-444, 2011
(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.
