Abstract
Distributions of dislocations creating point defects are considered. These point defects are described by a metric tensor, which supplements a Burgers field responsible for dislocations. The metric tensor depends on the distribution of dislocations and defines a Riemannian geometry of the material space of a continuized crystal and thus an internal length measurement in this crystal. The dependence of the distribution of dislocations on the existence of point defects created by these dislocations is modeled by treating the Burgers field as a field defined on the Riemannian material space. Field equations, following from geometric identities, are formulated as balance equations on this Riemannian space and their source terms, responsible for interactions of dislocations and point defects, are identified.
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Trzesowski, A. Dislocations and internal length measurement in continuized crystals. I. Riemannian material space. Int J Theor Phys 33, 931–950 (1994). https://doi.org/10.1007/BF00672825
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DOI: https://doi.org/10.1007/BF00672825