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A proposal for defining continuous distribution of dislocations for objective structures

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Abstract

Though targeting at different scales, the theory of objective structures and the theory of materially uniform bodies have some issues in common. We highlight those aspects of the two theories that share similar ideas, as well as delineate areas where they are inherently different. Prompt by the fact that materially uniform but inhomogeneous bodies ultimately describe dislocations into solids, we propose a way for defining continuous distribution of dislocations for objective structures. In the course of doing, so we draw upon combined theories of algebraic topology and discrete exterior calculus to model crystal elasticity. We also need a generalization of the theory of materially uniform bodies suitable for a class of micromorphic bodies.

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Author information

Correspondence to Dimitris Sfyris.

Additional information

Communicated by Andreas Öchsner.

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Sfyris, D. A proposal for defining continuous distribution of dislocations for objective structures. Continuum Mech. Thermodyn. 27, 399–407 (2015). https://doi.org/10.1007/s00161-014-0362-9

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Keywords

  • Objective structures
  • Materially uniform bodies
  • Inhomogeneous bodies