Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1998-10-08
2004-01-13
Jones, Hugh (Department: 2123)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S001000, C703S007000
Reexamination Certificate
active
06678642
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates to the field of modeling interactions, specifically modeling interactions where part of a problem space remains topologically consistent while another part can undergo topological disruption. This invention relates more specifically to the field of using a computer to model interactions between a hard material and a soft material.
Soft/hard interactions are a set of engineering problems in which a rigid body interacts with a softer material. A hard metal die D forming a softer metal or plastic P, as illustrated in
FIG. 1
, is an example of this sort of interaction. Soft/hard interactions can be difficult to model because of the very different behaviors of the two materials. In particular, detailed modeling of tribological effects and internal functions in the hard material can best be done in a Lagrangian framework, while accurate modeling of the bifurcating soft material can best be done in an Eulerian framework.
The difficulty of modeling a bifurcating flow field using a Lagrangian mesh arises from the topological aspects of the bifurcation. A continuous flow field, free of bifurcations, changes the shape of a body without changing the connectivity of the body. Surface points remain on the surface, interior points remain in the interior, and neighboring points remain neighbors. This allows an analytic function to map the final configuration of the material back to the original configuration. Such functions are easily represented on a discrete mesh.
A bifurcation, however, produces a discontinuity on the flow field. Neighboring points on either side of the bifurcation are no longer neighbors, and new surface points are created that do not map to any surface in the original configuration. A static Lagrangian mesh, in which the connectivity does not change, thus can not model the bifurcating behavior. Either the mesh must be Eulerian, for which mapping between initial and final configurations is not required, or a method must be employed to reconnect the Lagrangian mesh and correctly capture the topology of the bifurcation.
It is theoretically possible to model soft/hard interactions with Eulerian meshes, but the results can be disappointing. A large number of cells are required to represent thin structures and small components, and sophisticated interface trackers can be required to preserve material interfaces. Velocity discontinuities at the soft/hard interface are not well represented. Resulting models can be expensive, and can lack accuracy and robustness.
Several methods have been proposed for modeling soft/hard interactions, including a posterior methods, heterogeneous mesh methods, free Lagrange methods, and smooth particle hydrodynamics methods.
a posterior methods assume that the line of bifurcation is known in advance. A “pilot hole” is positioned along the line of bifurcation and conventional contact surfaces defined between the rigid body and the sides of the pilot hole. Because a posterior methods require advance knowledge of the line of bifurcation, they cannot be readily used to model complex or unknown trajectories. Further, the mechanical work required to create the bifurcation is not correctly modeled. Also, localized strain around the bifurcation can make generation of suitable meshes very difficult.
In a heterogeneous mesh method an Eulerian mesh is used to represent the soft material and a Lagrangian mesh is used to represent the hard material. A transition mesh (usually referred to as an ALE or arbitrary Lagrangian-Eulerian mesh) is used to join the two regions. Bifurcation usually occurs along the boundary between the hard Lagrangian material and the soft Eulerian material, however, leaving no place for the transition region if the Eulerian and Lagrangian boundaries are to coincide.
Free Lagrange methods dynamically change the connectivity of a Lagrangian mesh to represent bifurcation. A successful free Lagrange method must detect bifurcating points, determine the direction of propagation of a bifurcation, and change the mesh connectivity. Detection of bifurcating points can be difficult, and determining the direction of bifurcation can be even more difficult. Without accurate, robust techniques for detection of bifurcations and determination of bifurcation direction free Lagrangian methods are limited in application.
A smooth particle hydrodynamics method eliminates the concept of a mesh representation for the soft material. The hard material is represented in a Lagrangian mesh, but the soft material is represented by a set of particles that interact through a smooth potential with their neighbors. The interaction between hard and soft materials can be modeled with a straightforward contact method. Unfortunately, there is shot noise from the statistical nature of the smooth particle interactions, and there is a strong tendency for the soft material to behave as a viscous liquid rather than a soft solid.
Accordingly, there is a need for method and apparatus for modeling interactions that can accurately model tribological and other properties and can accommodate topological disruptions.
SUMMARY OF THE INVENTION
The present invention provides a method and apparatus for modeling interactions that accurately models tribological and other properties and accommodates topological disruptions sound.
In a method according to the present invention, a first portion of a problem space is represented with a Lagrangian mesh. The first portion can, for example, correspond to a hard material. A second portion of the problem space is represented with an arbitrary Lagrangian-Eulerian (ALE) mesh. An ALE mesh can adaptively behave as a Lagrangian mesh, an Eulerian mesh, or anything in between. In the present invention, the ALE mesh behaves much like an Eulerian mesh but adapts to maintain correspondence between the Lagrangian and ALE contact surfaces. The second portion can, for example, correspond to a soft material. The first and second portions are substantially non-overlapping, and together can cover the entire problem space. The ALE and Lagrangian meshes are constructed so that each node on the surface of the Lagrangian mesh is in a known correspondence with adjacent nodes in the ALE mesh. The interaction is predicted for a time interval, for example by a finite element mechanical simulation of a hydrodynamics simulation. The prediction provides predicted locations for the nodes in the two meshes. The prediction step can enforce contact constraints, including enforcing contacts that might otherwise cause the meshes to overlap. The nodes in the ALE mesh in correspondence with nodes on the surface of the Lagrangian mesh are then mapped so that they are once again adjacent to their corresponding Lagrangian mesh nodes. The ALE mesh can then be smoothed to reduce mesh distortion that might reduce the accuracy or efficiency of subsequent prediction steps. The process, from prediction through mapping and smoothing, can be repeated until a terminal condition is reached.
The present invention also comprises a method for using a computer to model interactions. Representations using ALE and Lagrangian meshes, as discussed above, are loaded into or generated on the computer. The prediction step can be accomplished with simulation codes known to those skilled in the art. The computer can then be directed to map and smooth the ALE nodes as discussed above.
The present invention also comprises an apparatus for modeling interactions. A processor connects with an input/output system and storage. The apparatus further comprises means for representing, in storage, representations of portions of the problem space in ALE and Lagrangian meshes, means for predicting the locations of the mesh nodes after a time interval, means for mapping the nodes after prediction, and means for smoothing the ALE mesh, which can comprise computer software, hardware, or network downloads.
Advantages and novel features will become apparent to those skilled in the art upon examination of the following description or may be learned by practice of the invention
Bieq Kevin W.
Grafe Y. Gerald
Jones Hugh
Sandia Corporation
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