Contact modeling using step boundary method for immersed boundary finite element method

Immersed boundary finite element method (IBFEM) seeks to use accurate geometry of structures defined using equations of its boundaries and immersed in a background mesh for finite element analysis. The background mesh is non-conforming and is often a uniform Cartesian mesh which is used to approximate the trial solution. A variety of approaches to apply boundary conditions and evaluate stiffness have been proposed in the literature. A method for modeling contact between solids for IBFEM is presented where the equations of the contacting boundaries are used to construct trial solutions that satisfy contact conditions at the interface between solids. The method is applied here for small deformation elastic problems to model tied contact with or without initial gap or interference between the undeformed geometry of the objects. This approach is particularly suited for IBFEM because the background mesh does not conform to the geometry of the analysis domain and the nodes of the mesh may not be on the boundaries or the contact interfaces. Several contact problems that have analytical solutions are used here to validate the step boundary method.