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Application of variational and fem methods to the modelling and numerical analysis of the slitting process for geometrical and physical nonlinearity

Bohdal Ł., Kukiełka L.

Journal of Theoretical and Applied Mechanics

2015

Vol. 53 nr 2

487--500

Finite element modelling provides a great deal of support in the understanding of technological processes. However, there are few studies of the slitting process, and those that exist are simplified for use only in the calculation of steady states of such processes. This paper proposes the application of variational and finite element methods for the analysis of slitting and the nonlinearities of this process. Physical and mathematical models of the process and a new thermo-elastic/thermo-visco-plastic material model are elaborated. The procedure is implemented in the finite element code ANSYS/LS-DYNA and the model is validated comparing the numerical and experimental results. The influence of various process conditions on the strain and stress states and the quality of the final product are analysed. The results lay the groundwork for further study regarding the numerical analysis of spring-back behaviour and the effect of tool elasticity on the quality of the final workpiece.

Representing a non-associated constitutive law by a bipotential issued from a Fitzpatrick sequence

Vallée C., Lerintiu C., Fortuné D., Atchonouglo K., Ban M.

Archives of Mechanics

2009

Vol. 61, nr 3-4

325-340

We analyze the relation between Géry de Saxcé's bipotentials representing non-associated constitutive laws and Fitzpatrick's functions representing maximal monotone multifunctions. We illustrate by two examples (one linear and monotone, the other non-linear and non-monotone) the fact that Fitzpatrick's representation coming from convex analysis provides a constructive method to discover the "best" bipotential modelling of a given Implicit Standard Material.