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NonEuclidean Models of Elastoplastic Materials with Structure Defects: Transition from Euclidean Model of Elastic Continuous Me,Used
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"If the world is meaningless that prevents invent any sense?"Lewis Carroll ?Alice's Adventures in Wonderland?. About 50 years ago importance to apply differential geometry for extending the elastic continuous medium model was recognized by researchers. The introduced affinemetric objects characterize the internal geometric structure of the continuous media and its difference from the Euclidean geometry. The affine metric objects are the internal variables, and they can't be measured directly. This book shows how to establish the relation between the nonEuclidean geometric parameters of description and experimentally measured characteristics. It is demonstrated on the basis of the nonequilibrium thermodynamics formalism that to determine the affinemetric characteristics it is experimentally sufficient to measure two independent functions: internal energy and dissipation function. The proposed approach allows us to construct a thermomechanical model of a continuous medium including a full set of nonEuclidean characteristics which corresponds, from the physical point of view, to the description of dislocations, disclinations and point defects.
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