Nefussi, G.; Proslier, L.; Gilormini, P. A simulation of cold-roll forming for elastoplastic materials. (English) Zbl 0905.73063 Int. J. Mech. Sci. 40, No. 1, 15-25 (1998). In our formulation, the metal sheet is considered as a thin shell, and its middle surface is described as a Coons patch depending on one geometrical parameter. Moreover, the material satisfies a constitutive rate equation in which the corotational rate of stress is used. We use the Prandtl-Reuss model, including the von Mises yield criterion and the normality flow rule. In order to integrate the elastoplastic constitutive equations, a radial return scheme is adapted so that the plastic power rate is calculated using a Gauss method. Its minimization gives the optimal shape for a strain hardening elastoplastic material, as well as the optimal velocity field. This approach has been implemented on a workstation and, as for rigid-plastic materials, it gives a very fast simulation of the cold-roll forming process. Cited in 1 Document MSC: 74A55 Theories of friction (tribology) 74M15 Contact in solid mechanics 74C99 Plastic materials, materials of stress-rate and internal-variable type 74S30 Other numerical methods in solid mechanics (MSC2010) Keywords:Coons patch; geometrical parameter; constitutive rate equation; corotational rate of stress; Prandtl-Reuss model; von Mises yield criterion; normality flow rule; radial return scheme; Gauss method; optimal shape; optimal velocity field PDFBibTeX XMLCite \textit{G. Nefussi} et al., Int. J. Mech. Sci. 40, No. 1, 15--25 (1998; Zbl 0905.73063) Full Text: DOI