Efficient isogeometric shell element with through-thickness stretch: application to incremental sheet forming

Jaro Hokkanen,Andrew J E Stephan,Michael C Elford,Dorival M Pedroso,Yunpeng Zhang

doi:10.1088/1742-6596/1063/1/012189

Jaro Hokkanen, Andrew J E Stephan + Show 3 more

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https://doi.org/10.1088/1742-6596/1063/1/012189

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Abstract

An isogeometric shell element with through-thickness stretch is applied to a two-point incremental forming problem. The shell element supports full three-dimensional constitutive laws and therefore does not make the plane stress assumption. An anisotropic material model is implemented to account for the sheet rolling direction. Automatically adjusting penalty stiffness is proposed for modeling the contact between the stylus tool and the sheet, whereas the die contact algorithm uses traditional constant penalty stiffness. A comparison is made between experimental results as well as results from a conventional shell formulation.

Highlights

Nonlinear problems such as automobile crash dynamics or sheet metal forming simulations often utilize the four-node, bilinearly interpolated Reissner-Mindlin shell elements combined with explicit time integration
Adjusting penalty stiffness is proposed for modeling the contact between the stylus tool and the sheet, whereas the die contact algorithm uses traditional constant penalty stiffness
The purpose of this paper is to evaluate the suitability of the aforementioned shell element to incremental sheet forming (ISF) using explicit time integration

Summary

Introduction

Nonlinear problems such as automobile crash dynamics or sheet metal forming simulations often utilize the four-node, bilinearly interpolated Reissner-Mindlin shell elements combined with explicit time integration. These Reissner-Mindlin elements imposing the plane stress condition have dominated the finite element shell analysis for decades. The use of bilinear interpolation functions has resulted in efficient formulations and larger stable time step sizes compared to higher-order Lagrange shell elements. The interest in more advanced formulations such as thickness stretchable shell elements and solid-shells has increased as the plane stress assumption is not always acceptable, if thick plates or problems involving doublesided contact are considered. The computational speed has yet to be improved for demanding problems such as incremental sheet forming

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