The paper presents an updated Lagrangian-type finite element procedure, formulated with reference to a surface embedded coordinated system. Membrane shell theory is employed, and an attempt is made to calculate the strain distribution incurred by a peripherally clamped square plate, when impressed by a rigid punch. Three different punch geometries were considered. The material is treated as a rate insentive, elastic work-hardening solid, which obeys the J2 flow theory; both finite deformation and normal anisotropy can be considered. A linear relationship between the Jaumann rate of Cauchy stress and the Eulerian rate of Green’s strain tensor is derived. A slip-stick model was adopted for the interfacial frictional conditions. This was achieved by considering the equilibrium of a constant strain-element node in contact with the tools, and deciding whether such a node would stick or slip under Coulomb friction conditions. It is demonstrated that the punch geometry and frictional conditions exert a strong influence on the deformation mode, and hence, upon the overall strain distribution. The predictions were checked against experimental observations when stretch-forming square plates of pure aluminum, 0.5-mm thick. Contours of equal height on the deforming blanks were determined using a Moir´e fringe technique. The agreement between theory and experiment was favorable.
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Finite Element Modeling of the Punch Stretching of Square Plates
Yatsushiro National College of Technology, Yatsushiro, Kumamoto, Japan
Department of Mechanical Engineering, McMaster University, Hamilton, Ontario, Canada
Nakamachi, E., and Sowerby, R. (September 1, 1988). "Finite Element Modeling of the Punch Stretching of Square Plates." ASME. J. Appl. Mech. September 1988; 55(3): 667–671. https://doi.org/10.1115/1.3125846
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