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E. Kocbay, Y. Vetyukov:
"Stress resultant plasticity for plate bending in the context of roll forming of sheet metal";
International Journal for Numerical Methods in Engineering, 122 (2021), 18; 25 S.

Modeling of roll forming process of sheet metal requires efficient treatment of plastic deformations of thin shells and plates. We suggest a new general approach toward constructing the governing equations of bending of an elastic-plastic Kirchhoff plate on the structural mechanics level. The generic function of the isotropic hardening law is formulated in terms of variables, which are meaningful for a material surface, namely resultant bending moments and dissipative work. This function is then identified by comparison of the exact solutions for a uni-axial or isotropic bending experiment within the structural model and with the continuum model of a through-the-thickness element. We validate the approach against both the fully three-dimensional simulations as well as the results of the traditional elastic-plastic plate analysis, the latter one featuring the continuum laws of plasticity treated in the integration points along the thickness direction. We considered benchmark problems from the literature as well as a prototype for the roll forming problem. Besides good agreement regarding the shape of plastic zones and force-deflection characteristics, experiments also demonstrate higher computational efficiency of the new stress resultant model.

elastic-plastic plate, finite element analysis, roll forming, stress resultant plasticity

http://dx.doi.org/10.1002/nme.6760

https://doi.org/10.1002/nme.6760