A Consistent Implicit Formulation for Nonlinear Finite Element Modeling With Contact and Friction: Part I—Theory

[+] Author and Article Information
M. J. Saran, R. H. Wagoner

Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210

J. Appl. Mech 58(2), 499-506 (Jun 01, 1991) (8 pages) doi:10.1115/1.2897212 History: Received July 11, 1990; Revised October 26, 1990; Online March 31, 2008


A formulation for finite element simulation of highly nonlinear problems including friction and contact with arbitrarily shaped rigid surfaces is proposed (CFS approach), prompted by difficulties in robust and accurate simulations of industrial forming processes. Nonlinearities are caused by large strains, plastic flow, and complex boundary conditions with frictional contact. In Part I the theoretical basis is described and the appropriate numerical algorithm is derived. The complete set of the governing relations, comprising equilibrium and interfacial equations, is appropriately linearized; resulting in a consistent tangent operator of the Newton-Raphson algorithm. In Part II, as a numerical verification, plane-strain sheet-forming processes are analyzed using a rigid-viscoplastic material model. Results are presented and discussed for test problems and for complex simulation of reverse drawing by concave tools.

Copyright © 1991 by The American Society of Mechanical Engineers
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