Вісник № 02. Динаміка і міцність машин
Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/44380
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Документ Simple shear: eigenvectors of Сauchy-Green tensors rotate against each other(Національний технічний університет "Харківський політехнічний інститут", 2019) Itskov, Mikhail; Larin, Oleksiy OleksandrovychSimple shear represents a somewhat complex case of deformation although it is very good studied. In this paper, we discuss a new aspect of simple shear which has not been observed before. Rotations of the eigenvectors of the right and left Cauchy-Green tensors with increasing amount of shear under the kinematically defined simple shear are theoretically studied. An analysis has been done within a framework of the nonlineartheory of elasticity. Mathematical processor Maple is used for the calculations and animation of the results. Phenomena of mutually opposite rotations of the eigenvectors of the right and left Cauchy-Green tensors is fond that can be important for anisotropic and in particular fibre-reinforced materials. We studied rotations of principal strain directions under the kinematically defined simple shear. Accordingly, eigenvectors of the right and left Cauchy-Green tensors rotate against each other with the increasing amount of shear. Interestingly, the eigenvectors of brotate in the same direction as line elements of the material while the eigenvectors of Cin the opposite direction. For example, this can be important for anisotropic and in particular fiber rein-forced materials. In this case, the direction of the maximal stretch will rotate with respect to reinforcement directions.