TAILIEUCHUNG - Duality in P rocess of noncommutative deformation and topological nature of cherepanov - rice integral
In this paper it is showed, that for the noncommutative deformation simultaneously there exist also loading deformation H, and unloading deformation Hv. The real deformation is a combination of these types of deformations. The criterion of destruction J reflects topological character of medium, . it defines properties of symmetry of medium at destruction. | Vietnam Journal of Mechanics, VAST, Vol. 31, No. 2 (2009), pp. 97 - 102 DUALITY IN P ROCESS OF NONCOMMUTATIVE DEFORM ATION A ND TOPOLOGICAL NATURE OF CHEREPANOV -RICE INTEGRAL Trinh Van Khoa Hanoi Architectural University Abstract. In t his paper it is showed, that for the noncommutative deformation simultaneously there exist also loading deformation H, and unloading deformation Hv. The real deformation is a combination of these types of deformations. The criterion of destruction J reflects topological character of medium, . it defines properties of symmetry of medium at destruction. It is possible to tell, that during destruction the energy is released not continuously but and discretely. This situation is reflected through topological number Q or nu mber of unloading, connected to him. 1. INTRODUCTION As known, after removal of loading an elastic body always comes back in an initial state. The given definition of elasticity is a little simplified. If , for example, the stress exceeds a limit of elasticity, the dependence between loading and deformation ceases to be linear and depends on the order of the application of loading [1]. For simplicity, it is supposed, that the equation of a curve rY = (e) is obtained at any program of the application of load, when the stress monotonously grows. Nevertheless for real materials it is more complicated. Let we have finished in loading up to a point A = (CY e of area of plasticity. After the unloading is made, t he stress rY decreases to zero. In this process it is reflected not only plastic behavior of material, but also elastic. More careful experiments have shown, that the law of unloading is not described precisely by straight line. Replacing it by its closest straight line, we find, t hat its inclination does not correspond in accuracy to the initial module of elasticity. For polymeric materials , and also at composite materials, for example, fibreglasses, the law of unloading differs from the Hooke's law very
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