Limit Analysis with Prescribed Velocities and Unilateral Conditions with Friction Applied in Scratch Test
Fabio da Costa Figueiredo1; Lavinia Maria Sanabio Alves Borges2
1 UFRJ/ CEFET-RJ; 2 UFRJ
doi:10.20906/CPS/COB-2015-0884
Resumo
The aim of this paper is to propose a limit analysis formulation with prescribed velocities in order to analyze problems under plastic collapse and evaluation of unilateral conditions with friction at the same boundary. Since two bodies are in contact and there is movement of one body in relation to the other, prescribing velocities seems more convenient than prescribing forces. Moreover, this proposed formulation evolves contact mechanics and unilateral restrictions of forces and velocities at the contact interface. Under Coulomb friction law, the bipotential proposed by De Saxcé is applied into limit analysis formulation in order to quantify the dissipation power by friction. Thereby, the external power applied by a tool in contact with a deformable body is not entirely converted into plastic power: some part of it is dissipated by friction. After deriving the limit analysis continuum formulation, a triangular discretization is proposed and the velocity and stress fields are interpolated. Then, the optimum conditions are deduced and the limit analysis problem is solved as an optimization problem, solved by an algorithm based on relaxation and contraction techniques. The contact problem is solved separately, by condensation of degrees of freedom technique and a complementarity problem is solved. As an application, the scratch test problem is modeled considering a rigid indenter in contact with a deformable body. The influence of friction on scratch hardness calculation is investigated as well as the occurrence of sliding or adhesion at the contact interface.
Palavras-chave: limit analysis; Unilateral contact; Friction