Three-dimensional finite element simulation of medium thick plate metal forming and springback

Degenerated shell element and membrane element have been widely applied in thin sheet metal forming analysis. However, for medium thick plate metal forming, especially in the case of typical double-sided contact problems such as local bulge forming or pure bending with a small radius, these two element models cannot accurately simulate normal extrusion deformation of the sheet metal. In this paper, a new finite element (FE) solver based on the solid-shell element dynamic explicit algorithm and implicit algorithm is developed for the simulation of medium thick plate metal forming and springback. The solid-shell element model considers bending effects with a thickness-direction multiple-point integration approach. The viscous damping hourglass control algorithm eliminates the spurious deformation modes activated by in-plane reduced integration (RI). The double sided contact analysis considering thickness variation describes the extrusion deformation in the thickness direction accurately. An improved plane-stress constitutive model in co-rotational configuration together with Hill's quadratic anisotropic yield criterion is employed to update the stress field. The solid-shell element obtains both solid-like and shell-like behaviours to simulate large membrane deformation, shear deformation and rotation. To test the performance of the solid-shell element, some numerical examples are taken and compared with experiments. The comparison results demonstrate that the solid-shell element model is competitive enough in the simulation of medium thick plate metal forming and springback. Highlights? A new finite element solver based on the solid-shell element is developed. ? The element model considers bending effects with a multiple-point integration method. ? The viscous damping method eliminates the hourglass modes. An improved plane-stress constitutive model is employed to update the stress field. ? The solid-shell element obtains both solid-like and shell-like behaviours.

[1]  Chahngmin Cho,et al.  Stability analysis using a geometrically nonlinear assumed strain solid shell element model , 1998 .

[2]  Antoine Legay,et al.  Elastoplastic stability analysis of shells using the physically stabilized finite element SHB8PS , 2003 .

[3]  Serge Cescotto,et al.  An 8-node brick element with mixed formulation for large deformation analyses , 1997 .

[4]  Brian L. Kemp,et al.  A four‐node solid shell element formulation with assumed strain , 1998 .

[5]  Frédéric Barlat,et al.  Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function , 2006 .

[6]  E. Ramm,et al.  Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept , 1996 .

[7]  Jeong Whan Yoon,et al.  Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one‐point quadrature solid‐shell elements , 2008 .

[8]  K. Y. Sze,et al.  A stabilized hybrid-stress solid element for geometrically nonlinear homogeneous and laminated shell analyses , 2002 .

[9]  Ying-hong Peng,et al.  A stabilized underintegrated enhanced assumed strain solid-shell element for geometrically nonlinear plate/shell analysis , 2011 .

[10]  Y. H. Kim,et al.  A partial assumed strain formulation for triangular solid shell element , 2002 .

[11]  T. Pian,et al.  An eighteen-node hybrid-stress solid-shell element for homogeneous and laminated structures , 2002 .

[12]  Jeong Whan Yoon,et al.  On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations , 2007 .

[13]  R. M. Natal Jorge,et al.  Sheet metal forming simulation using EAS solid-shell finite elements , 2006 .

[14]  Stefanie Reese,et al.  A large deformation solid‐shell concept based on reduced integration with hourglass stabilization , 2007 .

[15]  Dong-Yol Yang,et al.  Earing predictions based on asymmetric nonquadratic yield function , 2000 .

[16]  Jeong Whan Yoon,et al.  A new one‐point quadrature enhanced assumed strain (EAS) solid‐shell element with multiple integration points along thickness: Part I—geometrically linear applications , 2005 .

[17]  Alain Combescure,et al.  SHB8PS––a new adaptative, assumed-strain continuum mechanics shell element for impact analysis , 2002 .

[18]  Jeong Whan Yoon,et al.  A new one‐point quadrature enhanced assumed strain (EAS) solid‐shell element with multiple integration points along thickness—part II: nonlinear applications , 2006 .

[19]  L. P. Bindeman,et al.  Assumed strain stabilization of the eight node hexahedral element , 1993 .