Tests For Multiple Materials Problems
Free (open access)
M Vable & M E Fox
Boundary Element Method has proven to have very good resolution for stress gradients that arise in elastostatic problems. Strong stress gradients can exist near the interface of two materials, particularly when the material properties change significantly. These gradients due to material changes can also interact with the gradients from geometric features such as corners and cracks. Experience with homogenous material has established that good resolution of gradients require a graded mesh, but mesh refinement techniques are difficult to implement formul-tiple materials. There exists ample analytical, experimental, and numerical results for stresses near a perfectly bonded interface that can be used for validating boundary element method algorithms for multiple materials. However the complexity in the results due to factors described above make these tests less than desirable in the early stages of algorithm design and testing. This paper will present several simple tests that can simulate different types of interface conditions that range from the conventional continuity of tractions and displacements at a perfectly bonded interface to conditions that permit jumps in displacements or tractions in either the normal or tangential directions at the interface. The synopsis of the analytical solutions is presented in two tables for use by other researchers.