© Copyright by International OCSCO World Press. All rights reserved. 2006 VOLUME 17 ISSUE 1-2 July-August 2006 of Achievements in Materials and Manufacturing Engineering of Achievements in Materials and Manufacturing Engineering Short paper 245 An analytical incremental model for the analysis of the cup drawing H. Gharib*, A.S. Wifi, M. Younan, A. Nassef Mechanical Engineering Department, The American University in Cairo, 113 Kasr el Aini Street, Cairo 11511, Egypt * Corresponding author: E-mail address: hossam@aucegypt.edu Received 15.03.2006; accepted in revised form 30.04.2006 Analysis and modelling AbstrAct Purpose: of this paper Develop an analytical model for the cup drawing process to solve for the induced stresses and strains over the deforming sheet at any stage of deformation until a full cup is formed. Design/methodology/approach: An analytical model is developed for the cup drawing process by determining the variation of stresses and strains over the deforming sheet. The model uses finite difference approach and numerical procedures to solve for equilibrium, continuity, and plasticity equations in an incremental fashion. Findings: The developed analytical model results showed good correlation with experimental ones from the literature. Also, the analytical model was found to be useful in conducting parametric studies in order to determine how the different process parameters can affect the deforming cup. Research limitations/implications: This paper includes the development of an analytical model to analyze the deep drawing of axisymmetric cups. This model is then used as the solution engine for the optimization of the blank holder force for such cups avoiding failure by wrinkling or tearing. This model also gives an insight of the modes of deformation in the deep drawing process. Practical implications: This paper is part of a procedure that leads to the optimization of the blank holder loading scheme. The full procedure as presented in the two parts of the work may be applied in industry to minimize the maximum punch load or the work done during deep drawing process by modifying the blank holder force and at the same time avoid failures by wrinkling or tearing. Originality/value: Developing a predictive/corrective technique for solving the unknown boundaries of the deforming sheet. Keywords: Numerical techniques; Computational mechanics; Plastic forming; Cup drawing 1. Introduction The cup drawing is a basic deep drawing process. Thus, understanding the mechanics of the cup drawing process helps in determining the general parameters that affect the deep drawing process. There are mainly two methods of analysis; experimental and analytical/numerical. Experimental analysis can be useful in analyzing the process to determine the process parameters that produce a defect free product. However, experimental work is usually very expensive and time consuming to perform. On the other hand, the Analytical/Numerical modeling can be used to model and analyze the process through all stages of deformation. This approach is less time consuming and more economical than experimental analysis. There have been several efforts to solve and analyze the deep drawing problem [1-11]. Among these are the attempts to analyze the cup drawing process, which include the works of Chung and Swift [1], Woo [2-4] and Reissner and Ehrismann [5]. They developed analytical models for the cup drawing process to solve for stresses and strains over the deforming sheet metal. However, they did not explain how to determine the moving boundaries in the deforming sheet, which will be discussed later in this study. In the present study, an incremental Analytical/Numerical modeling approach is developed. The model analyzes the stresses and strains in the cup drawing process. It is established on the 1. Introduction