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Interaction and Multiscale Mechanics Volume 6, Number 2, June 2013 , pages 237-255 DOI: https://doi.org/10.12989/imm.2013.6.2.237 |
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Metal forming analysis using meshfree-enriched finite element method and mortar contact algorithm |
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Wei Huand C.T. Wu
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| Abstract | ||
| In this paper, a meshfree-enriched finite element method (ME-FEM) is introduced for the large deformation analysis of nonlinear path-dependent problems involving contact. In linear ME-FEM, the element formulation is established by introducing a meshfree convex approximation into the linear triangular element in 2D and linear tetrahedron element in 3D along with an enriched meshfree node. In nonlinear formulation, the area-weighted smoothing scheme for deformation gradient is then developed in conjunction with the meshfree-enriched element interpolation functions to yield a discrete divergence-free property at the integration points, which is essential to enhance the stress calculation in the stage of plastic deformation. A modified variational formulation using the smoothed deformation gradient is developed for path-dependent material analysis. In the industrial metal forming problems, the mortar contact algorithm is implemented in the explicit formulation. Since the meshfree-enriched element shape functions are constructed using the meshfree convex approximation, they pose the desired Kronecker-delta property at the element edge thus requires no special treatments in the enforcement of essential boundary condition as well as the contact conditions. As a result, this approach can be easily incorporated into a conventional displacement-based finite element code. Two elasto-plastic problems are studied and the numerical results indicated that ME-FEM is capable of delivering a volumetric locking-free and pressure oscillation-free solutions for the large deformation problems in metal forming analysis. | ||
| Key Words | ||
| meshfree; finite element; nonlinear; near-incompressible; plasticity; contact | ||
| Address | ||
| Wei Huand C.T. Wu : Livermore Software Technology Corporation, 7374 Las Positas Road, Livermore, CA 94551, USA | ||
