GALCIT Colloquium

We describe our approach to simulating curvilinear brittle fractures in two-dimensions based on the use of Universal Meshes.  A Universal Mesh is one that can be used to mesh a class of geometries by slightly perturbing some nodes in the mesh, and hence the name universal.  In this way, as the crack evolves, the Universal Mesh is always deformed so as to exactly mesh the crack surface.  The advantages of such an approach are: (a) no elements are cut by the crack, (b) new meshes are automatically obtained as the crack evolves, (c) the crack faces are exactly meshed with a conforming mesh at all times, and the quality of the surface mesh is guaranteed to be good, and (d) apart from duplicating degrees of freedom when the crack grows, the connectivity of the mesh and the sparsity of the associated stiffness matrix remains unaltered.

In addition to the mesh, we are now able to compute stress intensity factors with any order of convergence, which gives us unprecedented accuracy in computing the crack evolution.  As a result, we observe first order convergence of the crack path as well as the tangent to the crack path in a number of different examples.

In the presentation I will introduce the notion of a Universal Mesh, illustrate the progress we have made so far with some examples, and then focus on the simulation of curvilinear fractures, and on the tools we created to compute stress intensity factors.  In particular, show examples in which the computed crack path converge to the exact crack path, regardless of the mesh.  If time permits, simulation of thermally induced fracture and hydraulic fractures will be discussed.