Stress Fields near a Circular Hole in a Porous Medium Under Plane Deformation
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ss Fields near a Circular Hole in a Porous Medium Under Plane Deformation E. V. Lomakina,b,* and N. G. Minaeva,** a
b
Lomonosov Moscow State University, Moscow, 119991 Russia Moscow Aviation Institute (National Research University), Moscow, 125080 Russia *e-mail: [email protected] **e-mail: [email protected] Received January 20, 2020; revised January 24, 2020; accepted January 30, 2020
Abstract—An analysis of the properties of the constitutive equations of the theory of plasticity for porous media using Green’s yield criterion is carried out. It is shown that this criterion is one of the possible yield criteria for materials with plastic properties depending on the type of stress state, with the only difference being that the coefficients depend on the porosity parameter. Therefore, the yield criterion can be represented in an appropriate generalized form using a parameter of the form of the stress state, which is the ratio of the hydrostatic stress component to the effective von Mises stress, called in the literature the stress triaxiality. A semi-analytical solution to the problem of a space with a cylindrical hole under plane strain conditions is obtained. The stress distributions corresponding to the obtained solution is compared with the stress distributions in a similar problem for a solid, which plastic properties are invariant to the type of the stress state. The effect of porosity on the stress distribution and the size of the plastic region is investigated. Keywords: plasticity, plane deformation, Green’s yield criterion, space with a cylindrical hole, stress distribution DOI: 10.3103/S0025654420030073
1. INTRODUCTION Porous materials are widely used in various branches of modern engineering and allow the creation of lightweight and sufficiently durable structures with high energy absorption characteristics. Therefore, the study of the characteristic features of the stress distribution in the vicinity of various holes is important and this is the main goal of this work. Studies of the influence of the heterogeneity of the structure of these structural materials on their deformation, plastic, and strength properties have been the subject of studies by many authors [1–5]. When formulating the yield criterions in most models, the influence of the third invariant of the stress tensor was neglected and the yield surface was represented as a function of the second invariant of the stress deviator and the first invariant of the stress tensor, whose coefficients depended on the porosity parameter, which is the ratio of the void volume to the total volume of the material [1, 6–10]. With a quadratic dependence of the yield condition on the components of the stress tensor, the yield surface in the space of principal stresses was the surface of an elongated ellipsoid. These assumptions were confirmed by the results of experimental studies obtained under conditions of triaxial compression of various porous materials. To analyze the soils behavior, a linear relationship between the second stress deviator invariant
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