Study of discontinuities in solutions of the Prandtl–Reuss elastoplasticity equations
Tóm tắt
Relations across shock waves propagating through Prandtl–Reuss elastoplastic materials with hardening are investigated in detail. It is assumed that the normal and tangent velocities to the front change across shock waves. In addition to conservation laws, shock waves must satisfy additional relations implied by their structure. The structure of shock waves is studied assuming that the principal dissipative mechanism is determined by stress relaxation, whose rate is bounded. The relations across shock waves are subject to a qualitative analysis, which is illustrated by numerical results obtained for quantities across shocks.
Tài liệu tham khảo
A. G. Kulikovskii and A. P. Chugainova, “Shock waves in elastoplastic media with the structure defined by the stress relaxation process,” Proc. Steklov Inst. Math. 289, 167–182 2015.
D. B. Balashov, “Simple waves in Prandtl–Reuss equations,” J. Appl. Math. Mech. 56 (1), 107–116 1992.
A. G. Kulikovskii and A. P. Chugainova, “The overturning of Riemann waves in elastoplastic media with hardening,” J. Appl. Math. Mech. 77 (4), 350–359 2013.
V. M. Sadovskii, Discontinuous Solutions in the Dynamics of Elastoplastic Media (Nauka, Moscow, 1997) [in Russian].
V. M. Sadovskii, “Elastoplastic waves of strong discontinuity in linearly hardening media,” Mech. Solids 32 (6), 88–94 1997.
V. M. Sadovskii, “On the theory of shock waves in compressible plastic media,” Mech. Solids 36 (5), 67–74 2001.
G. I. Bykovtsev and L. D. Kretova, “Shock wave propagation in elastic-plastic media,” J. Appl. Math. Mech. 36 (1), 94–103 1972.
B. A. Druyanov, “Generalized solutions in the theory of plasticity,” J. Appl. Math. Mech. 50 (3), 367–372 1986.
S. K. Godunov and E. I. Romenskii, Elements of Continuum Mechanics and Conservation Laws (Nauchnaya Kniga, Novosibirsk, 1998) [in Russian].
V. N. Kukudzhanov, “Nonlinear waves in elastoplastic media,” Wave Dynamics of Machines, Ed. by K. V. Frolov (Nauka, Moscow, 1991), pp. 126–140.
A. G. Kulikovskii, “Surfaces of discontinuity separating two perfect media of different properties: Recombination waves in magnetohydrodynamics,” J. Appl. Math. Mech. 32 (6), 1145–1152 1968.