On the interaction of frictional formulations with bifurcation phenomena in hyperelastic steady state rolling calculations

A finite element formulation for hyperelastic steady state rolling of inflated tires is analyzed. In particular, numerical difficulties associated with enforcing frictional conditions within such a framework are discussed. We focus in this work on adherent (i.e., no slip) friction formulations, and in addition to analyzing the numerical difficulties associated with such problems, we also study the interaction of frictional conditions with bifurcation phenomena. Such phenomena are observed in the context of multiple solutions (both stable and unstable) of the discretized system, and are also manifested in the behavior of the iterative map used to solve the nonlinear algebraic system of equations.