Abstract
Several methods for solving dynamic problems of plane deformed state in elastoplastic statement are developed. Numerical solution was obtained for a material whose cross-section is shaped as a rectangle with a saw-cut crack in the middle (compact profile) in the case of three-point bending by using the finite difference method. Numerical results are illustrated by figures and tables. The obtained results are compared with the results of the problem of spatial and plane stress state. The values of plastic strains, stresses, principal stresses, and the Odquist parameter are given.
Similar content being viewed by others
References
V. I. Makhnenko, “Improvement of Methods for Estimation of Residual Life of Welded Joints in Durable Structures,” Avtomatich. Svarka, No. 10–11, 112–121 (2003) [Paton Welding J. (Engl. Transl.), No. 10–11, 107–116 (2003)].
V. R. Bogdanov, “Determination of Fracture Viscosity of a Material on the Basis of Numerical Modeling of Plane Deformed State,” Vestnik Kiev Nats. Un-tu. Ser. Fiz.-Mat. Nauki, No. 3, 51–56 (2008).
V. R. Bogdanov, “Three-Dimensional Dynamic Problem of Plastic Strain and Stress Concentration near the Crack Tips,” Vestnik Kiev Nats. Un-tu. Ser. Fiz.-Mat. Nauki, No. 2, 51–56 (2009).
V. R. Bogdanov and G. T. Sulim, “Determination of Fracture Viscisity of a Material on the Basis of Numerical Modeling of Three-Dimensional Dynamic Problem,” in Intern. Sci.-Techn. Collection of Papers “Reliability and Durability of Machines and Constructions”, No. 33, 153–166 (2010).
V. R. Bogdanov and G. T. Sulim, “Dynamic Development of Cracks by Compact Version of Elastoplastic Model of Plain Deformed State,” Vestnik Kiev Nats. Un-tu. Ser. Fiz.-Mat. Nauki, No. 4, 51–54 (2010).
V. R. Bogdanov and G. T. Sulim, “Modeling of Crack Motion by Solving the Problem of Plane Deformed State,” Vestnik Lviv Nats. Un-tu. Ser. Fiz.-Mat. Nauki, No. 73, 192–204 (2010).
V. R. Bogdanov and G. T. Sulim, “Modeling of Crack Extension by Numerical Solution of the Problem of Plane Deformed State,” Probl. Obchislov. Mekh. Mishchnosti Konstr., Dnepropetrovsk, No. 15, 33–44 (2011).
Yu. V. Nemirovskii and T.P. Romanova, “Dynamics of a Rigid-Plastic Curvilinear Plate of Varying Thickness with an ArbitraryHole,” Prikl. Mekh. 46(3), 70–82 (2010) [Int. Appl. Mech. (Engl. Transl.) 46 (3), 304–314 (2010)].
V. D. Kubenko and V. R. Bogdanov, “Planar Problem of the Impact of a Shell on an Elastic Half-Space,” Prikl. Mekh. 31(6), 78–86 (1995) [Int. Appl. Mech. (Engl. Transl.) 31 (6), 483–490 (1995)].
E. L. Zyukina, “Conservative Difference Schemes on Uniform Grids for Two-Dimensional Wave Equations,” in Proc. N. I. Lobachevskii Math. Center, Vol. 26 (Kazan, 2004), pp. 151–160 [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.R. Bogdanov, G.T. Sulim, 2013, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2013, No. 3, pp. 111–120.
About this article
Cite this article
Bogdanov, V.R., Sulim, G.T. Plain deformation of elastoplastic material with profile shaped as a compact specimen (dynamic loading). Mech. Solids 48, 329–336 (2013). https://doi.org/10.3103/S0025654413030096
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654413030096