Constraint softening for non-smooth node-to-segment contact
Node-to-segment formulations are widely used for solving problems involving contact between multiple solid bodies. An essential aspect of these formulations is ensuring the transition of the contacting node from one segment to the next. However, node-to-segment formulations are prone to numerical issues such as problems with convergence due to sudden changes in the contact force during such transitions. Most approaches in the literature utilize ad hoc techniques to resolve such issues, primarily by defining different special cases for different situations. In this study, a penalty-based formulation is used, in conjunction with a smoothed contact constraint, to overcome the numerical issues associated with such transitions. Further, to avoid ill-conditioning due to hard contact between multiple segments, a softening parameter is used to regularize the contact constraint. The proposed approach eliminates the need to distinguish between different special cases of node-to-segment contact and enables the use of a single formulation. In particular, problems involving contact between components of reticulated structures, modeled as a network of planar truss elements, are studied. These include contact between elements of a braced truss and the indentation and sliding of a cellular material with a lattice micro-structure. The performance of this approach, in terms of the error in contact enforcement, restoring forces, and the computational effort required, is studied with numerical examples of different types of non-smooth contact problems.
Prakash, Purdue University.
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