An Elastic-Perfectly Plastic Flow Model for Finite Element Analysis of Perforated Materials

Abstract

This paper describes the formulation of an elastic-perfectly plastic flow theory applicable to equivalent solid (EQS) modeling of perforated materials. An equilateral triangular array of circular penetrations is considered. The usual assumptions regarding geometry and loading conditions applicable to the development of elastic constants for EQS modeling of perforated plates are considered to apply here. An elastic-perfectly plastic (EPP) EQS model is developed for a fourth-order collapse surface which is appropriate for plates with a triangular array of circular holes. A complete flow model is formulated using the consistent tangent modulus approach based on the fourth-order function. The EPP-EQS method is used to obtain a limit load solution for a plate subjected to transverse pressure and fixed at the outer edge. This solution is compared to a solution obtained with an EPP-FEA model in which each penetration in the plate is modeled explicitly. The limit load calculated by the EPP-EQS model is 6 percent lower than the limit load calculated by the explicit model.