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Adaptive Remeshing for Sheet Metal Forming Simulations
Technical Paper
1995-20-0059
Sector:
Language:
English
Abstract
Finite element (FE) methods have been widely applied in creating
simulations of metal forming processes, as evidenced by the number
of major conferences dealing with this subject. The application of
computer simulations to manufacturing processes allows die
designers to evaluate their designs before the tools are
manufactured. In this way, simultaneous engineering can be applied
in a way that facilitates design for manufacturing.
To date, finite element methods have not entirely found their
way to the shop floor. Three-dimensional finite element analyses of
large deformation processes have been left in the hands of finite
element analysts. Finite element programs for these types of
applications are not currently (and might never become) black box
routines which can be run reliably by inexperienced modelers. For
reliable and predictive models, it is necessary that the input
parameters be selected by a knowledgeable user. One such input
parameter is the layout of the finite element mesh defining the
shape of the deforming blank.
Most sheet forming simulations involve a deformable blank that
contacts a comparably rigid set of tools. These tools may be
represented by computer-aided design (CAD) surface patches, or by a
mesh of nodes and elements that define the tooling surfaces.
Typically, these elements are considered rigid and do not change
shape during the analysis. Conversely, the blank must be defined by
nodes and elements that can change location and shape respectively
during the simulated forming. The size of these elements, and
therefore their number, must be carefully selected in order to
avoid large discretization errors.
Discretization errors are errors in the numerical solution that
result from the way continuous structures (the tools and the blank)
are represented by finite-sized discrete elements. In the tooling,
discretization errors typically result from using flat elements to
represent curvilinear surfaces. Using many elements will reduce the
discretization errors, but will increase the cpu costs.
Alternatively, the tools can be represented by analytical surfaces,
such as IGES or VDA surfaces. Provided that these surfaces are used
during the contact analysis, discretization errors in the tooling
can be eliminated.
The deformable blank must be represented by a mesh of nodes and
elements, and hence is subject to discretization errors. Large
elements tend to be stiffer than smaller elements, and hence
underpredict the strains in the blank. The finite element analyst
must be knowledgeable enough about the forming process to
understand which areas of the blank will undergo straining, and to
place enough small elements in these areas.
Additionally, large elements can introduce discretization errors
associated with contact between the blank and rigid tools,
particularly when the large elements in the blank contact smaller
elements that define a sharp feature on the tools. For most contact
algorithms, contact between the blank and tools is checked at the
nodes of the blank element. Nodes of the blank are checked for
penetration through the tooling surfaces. If a node is found to
penetrate an opposing surface, then a force or displacement is
imposed which tends to move the node back to the tooling surface.
If the element is large compared with the elements on the opposing
surface, it is possible for the opposing surfaces to intersect
without any correction of this condition. This is the situation
illustrated and can lead to significant discretization errors.
Discretization errors can be reduced by selecting many small
elements to represent the blank. However, the cpu cost associated
with using large numbers of elements can be prohibitive. For
instance, in implicit finite element codes such as ABAQUS Standard
the cpu cost rises as the fifth power of the mesh resolution. For
explicit FE codes such as LS-DYNA3D, the cpu cost rises as the
third power of the mesh resolution. Regardless of which FE code is
used, the number of elements must be carefully selected to balance
the computational costs against the required computational
accuracy.
This paper details some results of analyses using an adaptive
remeshing algorithm in LS-DYNA3D, a commercially available
nonlinear large-deformation finite element code. Comparisons are
made against results from more traditional models without adaptive
remeshing. A well-documented test geometry was used for the
comparison. This geometry was selected because it contains strain
paths from biaxial tension, through plane strain and into the
tensile strain regime.