Description: This paper describes the development of incipient yield and subsequent collapse surfaces for a plate containing a large number of small circular penetrations arranged in an equilateral triangular array. The collapse surface developed here is appropriate for formulating a generic elastic-plastic flow theory for perforated materials. A unit cell is defined to characterize the mechanical response of an equilateral triangular array of penetrations. An elastic-perfectly plastic [EPP] finite element analysis [FEA] computer program is used to calculate the EPP response of the unit cell. A sufficient number of load cases are solved to define the complete incipient yield and collapse surfaces for the unit cell. A fourth order yield function is defined by squaring the Von Mises quadratic yield function and retaining only those terms that are required for the symmetry dictated by the triangular array. Curve fitting is used to determine the coefficients of the fourth order function to match the incipient yield and collapse data calculated for the unit cell by FEA. The incipient yield function in the plane of the plate incorporating the penetration pattern is shown to be almost rhomboidal in shape while the collapse curve is more elliptical. The fourth order yield function which passes through the incipient yield data possess regions where the surface is concave--a concern when developing a plasticity theory based on the function. Fitting the coefficients of the fourth order function to the collapse data results in a curve which is shown to be always convex thus having all positive outward normal vectors which is a required property for the development of plasticity flow theories.
Date: February 1, 1999
Creator: Gordon, J.L.; Jones, D.P.; Hutula, D.N. & Banas, D.
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