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Simulation of necking at expansion of the circle cylinder. (Russian) Zbl 1119.35351

Stability of equilibrium of a circular cylinder which is made of homogeneous isotropic incompressible material at mono axial expansion and supercritical deformation of the cylinder are studied with use of exact three-dimensional equations of nonlinear elasticity. It is found that a homogeneous state of the cylinder loses the stability after reaching a maximum point on a tension diagram and is replaced then by an inhomogeneous rotationally symmetric state known as ”neck”, which will develop further.

MSC:

35Q35 PDEs in connection with fluid mechanics
74B10 Linear elasticity with initial stresses
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
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