Numerical method for solution of pointwise contact between surfaces

When computing pointwise contact between bodies in a numerical model, one has to define a gap quantity. This is evaluated along the model evolution to quantify contact contributions. In this context, the evaluation of the gap for a fixed configuration of the system is here denoted as the local contact problem (LCP). Present work discusses the LCP in the context of the master–master contact formulation between surfaces, which yields the solution of a four-variable set of nonlinear equations. We present and solve the LCP employing trust-region optimization methods, leading to a robust and general scheme. After, the developed method is applied for several examples of contact involving surface parameterizations, such as super-elliptical extruded surfaces in the context of beam-to-beam contact, arc-based extruded and revolved surfaces and NURBS surfaces for rigid body contact modeling. Applications are quite general, such as pointwise contact involving finite elements and contact between particles addressed by the discrete element method. The main contribution of present work is the discussion, characterization and a proposal for solution algorithm of the LCP in the context of the master–master contact between surfaces. This is fundamental for a successful use of master–master contact schemes.