Deformation and failure of originally isotropic media under the mises strength condition
- 23 Downloads
A model of an originally isotropic material is constructed from rigid particles — blocks. Any deformation of the model is presented as a sum of simple shears and lengthenings. Simple shears occur due to overcoming of friction forces on contact surfaces. The model does not assume an elastic or a quasi-elastic deformation in the second principal direction. Failure is considered as a decrease in resistance as strains increase. For the plane strain state, under the Mises strength condition, the equation of failure, the characteristics and the relations on the characteristics are determined, as well as the statements of the problem on failure are analyzed.
Unable to display preview. Download preview PDF.
- 1.S. B. Batdorf and B. Budiansky, “Mathematical theory of plasticity based on the concept of slip,” NACA, Tech. Note, No. 1871 (1949).Google Scholar
- 2.S. A. Khristianovich, “Deformation of a hardening plastic material,” Mekh. Tverd. Tela, No. 2 (1974).Google Scholar
- 3.E. I. Shemyakin, “Anisotropy in a plastic state,” Mekh. Syp. Sredy, 4, No. 4 (1973).Google Scholar
- 4.L. M. Kachanov, Fundamentals of the Plasticity Theory [in Russian], Nauka, Moscow (1969).Google Scholar
- 5.N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity [in Russian], AN SSSR, Moscow (1949).Google Scholar
- 6.A. I. Chanyshev, “On the effect of load application sequence in rock mechanics,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop. No. 4 (2000).Google Scholar
- 7.A. M. Zhukov, “Plastic strains under simple and complex loading of alloy AK-16,” in: Calculations of Strength [in Russian], Issue 12, Mashinostroenie, Moscow (1966).Google Scholar
- 8.A. A. Ilyshun, Plasticity. Fundamentals of the General Mathematical Theory [in Russian], AN SSSR, Moscow (1963).Google Scholar
- 9.A. I. Chanyshev, “To the problem of deformable medium failure. Part 1: Basic equations,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (2001).Google Scholar
- 10.A. A. Shvab, “Ill-defined problems of the elasticity theory,” Mekh. Tverd. Tela, No. 6 (1989).Google Scholar