A New Solid-shell Element And Its Complete-process Simulation Algorithm For Sheet Metal Stamping

In recent years, the finite element method has already become one of the most important numerical simulation methods, and numerical simulation softwares based on the finite element method have been widely applied in sheet metal stamping industry. In available commercial finite element numerical simulation softwares, sheet metal stamping processes are mainly simulated with membrane elements and shell elements. However, for thick sheet parts, with automobile structural components as their representatives, neither membrane elements nor shell elements can precisely describe their deformation behaviors. This is attributed to that both membrane elements and shell elements ignore the normal stress along the thickness direction and cannot embody the double-sided contact situations.Aiming to make up the shortcomings of membrane elements and shell elements, a new solid-shell element is proposed in this study. The dynamic explicit algorithm based on this element is constructed, and a set of solid-shell element sheet stamping complete-process simulation algorithms are developed. The complete-process simulation algorithms can not only reflect the compression effect of tools on sheet metal but also precisely describe the stress distribution along the thickness direction. Thus, the poor performance of available finite element softwares in treating non-plane-stress problems during sheet metal stamping can be perfected, and the simulation accuracy of forming simulation and springback prediction are remarkably improved.A new solid-shell element without locking phenomenon and hourglass mode is proposed in this study. By bringing in an Enhanced Assumed Strain (EAS) internal variable, both the volumetric locking and thickness locking of the element are eliminated. By adopting the four-point Assumed Nature Strain (ANS) interpolation, the trapezoidal locking and transverse shear locking are avoided. To eliminate the hourglass modes caused by in-plane single-point integration, both the strain transformation matrix and the covariant strain-displacement matrix are Taylor expanded, with their product projected and reconstructed. In this way, a physical stabilization method without over-stiffness is put forward. The calculation accuracy and convergence rate of the solid-shell element are validated with several classical linear benchmarks.The solid-shell element forming simulation algorithm in the dynamic explicit framework is established, and the convergence difficulties during analyzing large-deformation dynamic-contact problems such as drawing, bending, flanging and restriking are settled. An explicit condensation method with respect to the internal variable is proposed, which decreases the data storage effectively. To improve the computational efficiency of forming simulations, an adaptive mesh refinement strategy is designed for the solid-shell element, with the stability of the adaptive mesh guaranteed by the inheritance of hourglass stress. Elastic-plastic constitutive equations following Hill48, Y1d91, and Y1d2004-18p yield criterions are derived, providing preconditions for the deformation analyses of anisotropic sheet metals.Based on the proposed solid-shell element, a set of complete-process simulation algorithms for sheet metal stamping are finally developed and successfully applied to the simulation of forming, trimming/piercing and springback of automobile aluminum alloy structural parts and other thick-walled parts. To increase the dimensional accuracy of cutting edges, mesh refinement is adopted in the trimming/piercing algorithm. By employing advancing adjustment, mesh optimization and some other methods, mesh distortion is avoided. As for the static implicit springback algorithm without considering real tools, an element stabilization method in the implicit framework is deduced. Thus, the rank deficiency of stiffness matrix is eliminated while the precision of springback prediction is ensured. According to benchmark validation, the solid-shell complete-process simulation algorithms developed in this study can achieve favorable calculation accuracy and meet the requirements of practical applications.