Using finite volume models in 
moldfilling simulations

March 24, 2010

If you were thinking the only option for moldfilling analysis was the finite element variety, it’s worth your time to explore how finite volume simulation can increase accuracy in your models.

Most modern moldfilling simulation software uses some type of solid or shell element mesh to define the part geometry. These range from simple midplane element models meshed with 2D shells to 21⁄2D surface meshing strategies.

Increasingly, some of the higher-end software packages are using full 3D elements. With few exceptions, these codes almost exclusively use four-noded tetrahedral elements—not always the best choice when modeling fluid behavior.

Slideshow of figures 1-12.

As the fundamental physics of moldfilling simulation is really a fluid flow problem, several codes are now commercially available that use the finite volume method as opposed to the more common finite element method.

Finite element vs. 
finite volume
Most mold flow simulation is finite element based, a technology made popular in structural analysis codes. Some of the newer codes, such as Moldex3D, are finite volume. There is a significant difference in how these tools work.

The finite volume method differs in that the mesh grid nodes and integration points are fixed, and the fluid moves within the fixed mesh grid. In the finite element method, the mesh grid points actually move, simulating the flow behavior.

There are pros and cons to both approaches, the main practical advantage of finite volume codes being the accuracy of the solution for fluid flow and the speed with which you can get a solution. Finite element codes tend to be computationally expensive, as a large mesh can create inordinately large numbers of nodes, all of which must translate to simulate the flow behavior. Typically, the finite element method is more stable, and provides better results for those primarily interested in stress tensor outputs, such as in structural analysis. Finite volume codes are useful for fluid and gas flow problems, and are used extensively in CFD codes.

The speed advantage inherent in FV codes is significant for simulating thermoplastic flow when using full 3D elements, as it is necessary to create large numbers of elements to accurately capture the part geometry. For example, a good rule of thumb is to provide a mesh density of at least three 3D elements spanning the cross section of a wall thickness. Propagated over even a small part, this can create element counts in the hundreds of thousands, which can make it difficult to get timely solutions. Larger parts can and do create 3D element counts in the millions.

The use of finite volume technologies can substantially reduce the solution time to run these types of moldfill simulations. These jobs are very large, and the Moldex3D solver allows for parallel processing (we typically use an eight-core machine) to get a solution of a model this size in a few hours. Such a large model may not even run on an FE solver, and many moldfilling codes do not support parallel processing.

High-density 3D elements. Armed with a high-performance finite volume solver, we can now use high-quality 3D elements to model plastic flow, and get solutions in minutes or hours instead of days, with high-fidelity results. Figure 1 shows a moldfilling analysis using typical 2½D fusion elements, while Figure 2 shows the same part using high-order 3D elements in a finite volume solver. The differences are dramatic. With computationally efficient FV solvers, we can also expand our element library to include higher-order elements, such as hexahedrals, to capture much more accurate fluid flow behavior.

Drilling into the mesh resolution, we can see a typical high-order mesh in Figures 3, 4, and 5. Note that these mesh structures are a hybrid of several element types.

In addition to using these types of hybrid meshes, we can combine these methods into a boundary layer strategy, allowing higher-order elements to be used on the part bounding surfaces and lower-order 3D elements to be used in the part interior for better resolution of temperature effects on the critical boundary layer. An example can be seen in Figure 6.

Gate/runner modeling. One of the most important parts of moldfilling simulation is the gate and runner modeling. This is an area that is often overly simplified by software applications, and poor accuracy here can negatively influence results. Best results can be achieved using high-order 3D elements in the gate and runners as well as in the part geometry.
Results correlation. One of the best ways to validate the predicted results of a mold flow is to compare with a short shot study after the fact (Figures 7-9).

Fiber orientation and postprocessing. One of the more interesting aspects of this type of analysis is the ability to import moldfilling analysis results into structural analysis software for more realistic loads analysis. Most structural FEA uses the flawed assumption that thermoplastics are isotropic (uniform material properties) and therefore cannot accommodate the effects of molding on structural part performance. This can lead to unanticipated part failures when weldlines, material flow lines, and part density changes occur in highly loaded areas.

When the moldfilling solver runs the warp load case in a typical molding simulation, we (automatically) convert to the finite element method, as we are now interested in finite strains and residual stresses to predict warp accurately. This output file can then be used as an initial condition for a structural FEA, bringing along the
following attributes:
• Fiber orientation.
• Material density variations.
• Residual stresses (flow and thermally induced).
• Initial strain.

These attributes are critical to understanding the part performance when structural loads are applied. When coupled with orthotropic or anisotropic material data, accurate structural FEA can be performed on injection molded parts. Figure 10 depicts a cross section of a molding simulation showing fiber orientation of a glass-filled part, while Figures 11 and 12 show the warp prediction with and without consideration of fiber orientation.

John Cogger ([email protected] is president of Innova Engineering Inc. in Irvine, CA (, a full-service engineering firm specializing in nonlinear analysis of plastics.

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