# Computing pointwise contact between bodies: a class of formulations based on master–master approach

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## Abstract

In the context of pointwise contact interaction between bodies, a formulation based on surface-to-surface description (master–master) is employed. This leads to a four-variable local contact problem, which solution is associated with general material points on contact surfaces, where contact mechanical action-reaction are represented. We propose here a methodology that permits, according to necessity, a selective dimension reduction of this local contact problem. Thus, the formulation includes curve-to-curve, point-to-surface, curve-to-surface or other contact descriptions as particular degenerations of the surface-to-surface approach. This is done by assuming convective coordinates in the original local contact problem. An operator for performing the so-called “local contact problem degeneration” is presented. It modifies automatically the dimension of the local contact problem and related requirements for its solution. The proposed method is particularly useful for handling singularity scenarios. It also creates a possibility for representing conformal contact by pointwise actions on a non-uniqueness scenario. We present applications and examples that demonstrate benefits for beam-to-beam contact. Ideas and developments, however, are general and may be applied to other geometries of contacting bodies.

## Keywords

Contact Master–master Degeneration Optimization## Notes

### Acknowledgements

The first author acknowledges FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) under the Grant 2016/14230-6 and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) under the Grant 304680/2018-4.

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