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Validity Analysis of Elastic-Plastic Deformation Mechanics Problems Considering the Growth of Pores in the Material Via the Reiss–Tracey–Huang Models. Part 1. The Reiss–Tracey Model

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The conditions that ensure the validity of nonlinear problems of elastic-plastic deformation mechanics, taking into account the growth of nucleated pore volume in the material via the Reiss–Tracey model, are investigated. Using this model, the determinants of material behavior are formulated, making it possible to describe nonisothermal processes of elastic-plastic deformation considering the increased concentration of viscous fracture pores. The loading process is broken down into separate computational stages, within which the plastic flow equation and pore concentration growth equations via the specified model are integrated over the loading stage. Through integration, the constitutive equations for the full stress and strain components are derived, allowing one to describe the active loading, unloading, and re-loading processes. The irreversible strains in these equations include accumulated plastic strains and structural bulk strains, which account for the pore concentration in the material via the Reiss–Tracey model. The solution of practical problems via the formulated equations promotes the persistence of computational processes, making it possible to use extended loading stages in calculations. At the same time, the analysis of properties of the obtained determinative equations is simplified in comparison with the equations of plasticity in finite increments. Conditions are formulated, in which the dissipation power and the power developed by additional stresses and stress-induced on additional strains do not drop during the loading of porous materials. On the basis of the obtained energy inequalities, which generalize Drucker’s postulate with respect to the porous material, conditions are established that ensure the correctness of the formulated plasticity equations, which take into account the pore volume growth via the Reiss–Tracey model.

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  1. Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    O. Yu. Chirkov

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  1. O. Yu. Chirkov
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Correspondence to O. Yu. Chirkov.

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Translated from Problemy Mitsnosti, No. 3, pp. 5 – 17, May – June, 2022.

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Chirkov, O.Y. Validity Analysis of Elastic-Plastic Deformation Mechanics Problems Considering the Growth of Pores in the Material Via the Reiss–Tracey–Huang Models. Part 1. The Reiss–Tracey Model. Strength Mater 54, 345–357 (2022). https://doi.org/10.1007/s11223-022-00410-6

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