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All Outputs (12)

Connection and curvature in crystals with non-constant dislocation density (2018)
Journal Article
Parry, G. P., & Elzanowski, M. Z. (2019). Connection and curvature in crystals with non-constant dislocation density. Mathematics and Mechanics of Solids, 24(6), 1714-1725. https://doi.org/10.1177/1081286518791008

Given a smooth defective solid crystalline structure defined by linearly independent 'lattice' vector fields, the Burgers vector construction characterizes some aspect of the 'defectiveness' of the crystal by virtue of its interpretation in terms of... Read More about Connection and curvature in crystals with non-constant dislocation density.

Two-dimensional defective crystals with non-constant dislocation density and unimodular solvable group structure (2018)
Journal Article
Parry, G. P., & Zyskin, M. (2018). Two-dimensional defective crystals with non-constant dislocation density and unimodular solvable group structure. Journal of Elasticity, 1-39. https://doi.org/10.1007/s10659-018-9680-7

In Parry and Zyskin [1] we outlined mathematical methods which seemed to be necessary in order to discuss crystal structures with non-constant dislocation density tensor (ddt). This was part of a programme to investigate the geometry of continuously... Read More about Two-dimensional defective crystals with non-constant dislocation density and unimodular solvable group structure.

Geometrical structure of two-dimensional crystals with non-constant dislocation density (2016)
Journal Article
Parry, G. P., & Zyskin, M. (in press). Geometrical structure of two-dimensional crystals with non-constant dislocation density. Journal of Elasticity, 127(2), https://doi.org/10.1007/s10659-016-9612-3

We outline mathematical methods which seem to be necessary in order to discuss crystal structures with non-constant dislocation density tensor(ddt) in some generality. It is known that, if the ddt is constant (in space), then material points can be i... Read More about Geometrical structure of two-dimensional crystals with non-constant dislocation density.

Discrete structures in continuum descriptions of defective crystals (2016)
Journal Article
Parry, G. P. (2016). Discrete structures in continuum descriptions of defective crystals. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 374(2066), https://doi.org/10.1098/rsta.2015.0172

I discuss various mathematical constructions that combine together to provide a natural setting for discrete and continuum geometric models of defective crystals. In particular I provide a quite general list of `plastic strain variables', which quant... Read More about Discrete structures in continuum descriptions of defective crystals.

Group Elastic Symmetries Common to Continuum and Discrete Defective Crystals (2013)
Journal Article
Nicks, R., & Parry, G. P. (2014). Group Elastic Symmetries Common to Continuum and Discrete Defective Crystals. Journal of Elasticity, 115(2), 131-156. https://doi.org/10.1007/s10659-013-9450-5

The Lie group structure of crystals which have uniform continuous distributions of dislocations allows one to construct associated discrete structures—these are discrete subgroups of the corresponding Lie group, just as the perfect lattices of crysta... Read More about Group Elastic Symmetries Common to Continuum and Discrete Defective Crystals.

On symmetries of crystals with defects related to a class of solvable groups (S1) (2011)
Journal Article
Nicks, R., & Parry, G. P. (2012). On symmetries of crystals with defects related to a class of solvable groups (S1). Mathematics and Mechanics of Solids, 17(6), 631-651. https://doi.org/10.1177/1081286511427485

We consider distributions of dislocations in continuum models of crystals which are such that the corresponding dislocation density tensor relates to a particular class of solvable Lie group, and discrete structures which are embedded in these crysta... Read More about On symmetries of crystals with defects related to a class of solvable groups (S1).

Reconciliation of Local and Global Symmetries for a Class of Crystals with Defects (2011)
Journal Article
Parry, G. P., & Sigrist, R. (2012). Reconciliation of Local and Global Symmetries for a Class of Crystals with Defects. Journal of Elasticity, 107(1), 81-104. https://doi.org/10.1007/s10659-011-9342-5

We consider the symmetry of discrete and continuous crystal structures which are compatible with a given choice of dislocation density tensor. By introducing the notion of a 'defective point group' (determined by the dislocation density tensor), we g... Read More about Reconciliation of Local and Global Symmetries for a Class of Crystals with Defects.

Elastic symmetries of defective crystals (2010)
Journal Article
Parry, G. P. (2010). Elastic symmetries of defective crystals. Journal of Elasticity, 101(1), https://doi.org/10.1007/s10659-010-9254-9

I construct discrete and continuous crystal structures that are compatible with a given choice of dislocation density tensor, and (following Mal’cev) provide a canonical form for these discrete structures. The symmetries of the discrete structures ex... Read More about Elastic symmetries of defective crystals.

The structure of uniform discrete defective crystals (2006)
Journal Article
Cermelli, P., & Parry, G. P. (2006). The structure of uniform discrete defective crystals. Continuum Mechanics and Thermodynamics, 18(1-2), https://doi.org/10.1007/s00161-006-0019-4

In the continuum context, a uniform crystal has dislocation density tensor constant in space. A simple iteration procedure generates an infinite set of points which is associated with uniform defective crystals. When certain necessary conditions are... Read More about The structure of uniform discrete defective crystals.

Geometrical issues in the continuum mechanics of solid crystals
Journal Article
Nicks, R., & Parry, G. P. Geometrical issues in the continuum mechanics of solid crystals. Miskolc Mathematical Notes,

We shall outline geometrical and algebraic ideas which appear to lie at the foundation of the theory of defective crystals that was introduced by Davini [5] in 1986. The focus of the paper will be on the connection between continuous and discrete mod... Read More about Geometrical issues in the continuum mechanics of solid crystals.