# Comparative analysis of the linear and nonlinear rules of mixtures in modeling the stress state of a half-space

## Authors

• N. D. Yakovenko State University of Telecommunications, 03110, Kyiv, Ukraine, 7, Solomenska
• O. P. Chervinko S.P. Timoshenko Institute of Mechanics NAS Ukraine, 03057, Kyiv, 3 Nesterov Str.
• S. M. Yakymenko Central Ukrainian National Technical University, Kropyvnytskyi, 8 Prospekt Universytetskyi

## Abstract

In the present work we solve the axially symmetric problem of a half-space under thermal loading. The statement of the problem includes: Cauchy relations, equations of motion, heat conduction equation, initial conditions, thermal and mechanical boundary conditions. The thermomechanical behavior of an isotropic material is described by the Bodner–Partom unified model of flow generalized in the case of microstructure influence on inelastic characteristics of steel. To determine the parameters of the model corresponded to yield stress and yield strength the mixture rule is utilized. The problem is solved with using the finite element technique. The numerical realization of our problem is performed with the help of step-by-step time integration. Equations of the evolution for the inelastic flow model are integrated by the second-order Euler implicit method. The equations of motion are integrated by the Newmark method, whereas the heat-conduction equation is integrated by the first-order implicit method. We use quadrangular isoparametric elements. The parameters of a fine grid are chosen with the help of the criterion of practical convergence of the solutions. The stress state taking into account linear and nonlinear rules of mixtures is described.

Pages of the article in the issue: 94 - 97

Language of the article: Ukrainian

## References

SENCHENKOV, I. K., CHERVINKO, O. P., TURYK, E., RYABTSEV, I. (2008) Examination of the thermomechanical state of cylindrical components deposited with layers of austenitic and martensitic steels. Weld. Int. [Online] 22 (7). p. 457–464. Available from: https://doi.org/10.1080/09507110802352340

Rushchitsky, J. (1991) Elementy teorii smesej. Кiev: Naukova dumka.

BORJESSON, L., LINDGREN, L-E. (2001) Simulation of multipass welding with simultaneous computation of material properties. Trans of ASME I. of Eng. Mater. Techn. [Online] 123 (2). р. 106–111. Available from: https://doi.org/10.1115/1.1310307

SENCHENKOV, I. K., OKSENCHUK, N. D. (2013) Modeling of a nonisothermal flow with regard for the dependence of plastic properties on the microstructure of a material. J. Math. Sci. [Online] 190 (6). р. 796-803. Available from: https://doi.org/10.1007/s10958-013-1289-6

BOUQUEREL, J., VERBEKEN, K., DE COOMAN, B.C. (2006) Microstructure-based model for the static mechanical behavior of multiphase steel. Acta Materialia. [Online] 54 (46). р. 1143–1156. Available from: https://doi.org/10.1016/j.actamat.2005.10.059

ZHUK, Y. A., SENCHENKOV, I. K., KOZLOV, V. I., TABIEVA, G. A. (2001). Axisymmetric dynamic problem of coupled thermoviscoplasticity. Int. Appl. Mech. [Online] 37 (10). p. 1311–1317. Available from: https://doi.org/10.1023/A:1013976219144

2021-12-21

## How to Cite

Yakovenko, N. D., Chervinko, O. P., & Yakymenko, S. M. (2021). Comparative analysis of the linear and nonlinear rules of mixtures in modeling the stress state of a half-space. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (4), 94–97. https://doi.org/10.17721/1812-5409.2021/4.15

## Section

Differential equations, mathematical physics and mechanics