ar X iv : m at h - ph / 0 50 20 07 v 1 2 F eb 2 00 5 ON THE GEOMETRY OF A DISLOCATED MEDIUM
نویسندگان
چکیده
In [1] a phenomenological approach to the nonlinear theory of plasticity in glasses, pitches, and soft polymers was suggested (see also [2]). Currently, we have no direct microscopic support for the results of [1] since microscopic mechanisms of plasticity in amorphous materials are not yet completely understood, especially if one needs an exact quantitative description (see papers [3] and [4] where some approaches are developed, but this is by no means the ultimate theory). Having no direct way, one should maneuver choosing a detour, a roundabout course to the goal. For the theory of plasticity this course goes through the theory of dislocations (see [5–7]). The matter is that dislocations provide a microscopic mechanism explaining the plasticity of crystals. Relying on the integrity of the nature, one can expect that the plasticity phenomenon in crystals and in amorphous materials are described similarly. The paper [5] is a review of the basics. There the nonlinear elastic and plastic deformation tensors Ĝ and Ǧ for a crystalline medium are defined, and the following differential equations for them are derived:
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