Coupling Boundary Integral and Finite Element Formulations for Nonlinear Halfspace Problems

In finite element applications involving static or quasistatic nonlinear inelastic response in unbounded regions, there is the question of how to truncate the region to be modeled and how to select appropriate boundary conditions to be imposed on the remote boundary. An example of an application in which this problem arises is the determination of the history of the deformation of an underground tunnel due to creep. Typically such problems are modeled by placing the exterior boundary “far enough away” so that the effect of fixing the boundary does not significantly alter the stress and deformation in areas of interest. There are two drawbacks to this approach. First, there is always some effect no matter how far away the boundary is placed, which makes it difficult for the analyst to judge precisely how much effect his choice of the location of the boundary is having on the solution. This is especially true in non- linear problems where intuition often fails. The second and perhaps more important drawback is that the boundary must be placed so far away from regions of interest that an unnecessarily large number of elements must be used, which increases the computational cost of the analysis.