An Algorithm for Three-Dimensional Mesh Generation for Arbitrary Regions with Cracks

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Joaquim B. Cavalcante Neto, Marcelo T. M. Carvalho, Luiz F. Martha
Department of Civil Engineering and Computer Graphics Technology Group - TeCGraf, Pontifical Catholic University of Rio de Janeiro -- PUC-Rio, Rio de Janeiro, RJ 22453-900, Brazil

Paul A. Wawrzynek, Anthony R. Ingraffea
Cornell Fracture Group, Cornell University, 643 Rhodes Hall, 14853 Ithaca, NY
paw4@cornell.edu

Abstract
This paper describes an algorithm for generating unstructured tetrahedral meshes for arbitrarily shaped regions. The algorithm works for regions without cracks, as well as for regions with one or multiple cracks. The algorithm incorporates aspects of well known meshing procedures and includes some original steps. It includes an advancing front technique, but uses an octree procedure to develop local guidelines for the size of generated elements. The advancing front technique is based on a standard procedure found in the literature with two additional steps to ensure valid volume mesh generation for virtually any domain. To improve mesh quality (as far as element shape is concerned), an a posteriori local mesh improvement procedure is used.

The algorithm was designed to meet four specific requirements. First, the algorithm should produce well shaped elements, avoiding elements with poor aspect ratios, if possible. While the algorithm does not guarantee bounds on element aspect ratios, care is taken at each step to generate the best shaped elements possible.

The second requirement is that the algorithm generates a mesh that conforms to an existing triangular mesh on the boundary of the region. This is important in the context of crack growth simulation because it allows remeshing to occur locally in a region near a growing crack.

Many of the other meshing algorithms described in the literature generate the mesh on a region's boundary along with the volume mesh. As implied above, for the present algorithm a surface mesh is a required input. We do not consider this a significant limitation, however, because there are a number of good surface triangular mesh generators which can be used to generate the required surface mesh.

The third requirement of the algorithm is that it has the ability to transition well between regions with elements of very different sizes. In a crack analysis, it is not uncommon for the elements near the crack front to be two orders of magnitude smaller than other elements in the problem.

The fourth requirement is the specific modeling capability for handling cracks. This requirement arises because cracks are usually idealized as having no volume. That is, the surfaces representing the two sided of a crack face are distinct, but geometrically coincident. This means that nodes on opposite sides of crack faces may have identical coordinates. The algorithm must be able to discriminate between the nodes and select the one on the proper crack face.