Impact of a Cylinder Against a Rigid Target. Part II. Initial Condition.
An analysis of widely known Taylor's experiment that concerns the impact of short deformable cylinders made of a rigid-viscoplastic material against the rigid target, is performed. The case of axi-symmetric geometry with finite deformations and radial inertia is considered. The velocity initial condition given by the jump of the vertical component of the field does not belong to the problem solution as the equations describing the problem do not permit the first order discontinuity. To create the procedure initiating a numerical algorithm for this impact problem, the idea of a thin viscoplastic layer is introduced and a parametric approximation of the velocity field in a power form is proposed. The velocity field obtained from the approximation approches for t → t0 the profile characteristic for the viscoplastic model.
G.I. TAYLOR, The use of flat-ended projectiles for determining dynamic yield stress, Proc. Roy. Soc. Lond., 194, A, 300-332, 1948.
G.I. BARENBLATT and A.JU. ISLINSKIJ, lmpact of a visco-plastic rod on a rigid wall [in Russian], Prikl. Mat. Mech., 26, 497-502, 1962.
J. BEJDA, Analysis of deformation in a short visco-plastic cylinder striking a rigid target, AMS, 15, 6, 879-888, 1963.
T.C.T. TING, lmpact of a nonlinear viscoplastic rod on a rigid wall, J. Appl. Mech., Trans ASME, Ser. E, 33, 3, 505-513, 1966.
T. HAYASHI, H. FUKUOKA and H. TIDA, Axial impact of low carbon mild steel rod, Bull. JSME, 14, 75, 901-908, 1971.
W. KOSIŃSKI and A. NOWIŃSKA, lmpact of a cylinder against a rigid target. Part I. Compatibility conditions and the viscoplastic region evolution, Engng. Trans., 39, 1, 31-48, 1991.
A. NOWIŃSKA, The discrete model for the computer simulation of the rigid-viscoplastic rod impact onto a rigid target, [dissertation part II].
P. PERZYNA, The constitutive equations for rate-sensitive plastic materials, Q. Appl. Math., 20, 321-332, 1963.
T.C.T. TING and P.S. SYMONDS, lmpact on rods of non-linear viscoplastic material - numerical and approximate solutions, Int. J. Solids Structures, 3, 587-605, 1967.
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