Towards realistic simulation of deformations and stresses in pneumatic tyres

The paper presents a full three-dimensional finite element model of pneumatic tyre. The inclusion of a special node to the model enabled to analyse the problem of static tyre-road contact under vertical, lateral or longitudinal external forces. The hyperelastic properties of rubber are described with the use of the elastic strain energy density function in the form of the third degree polynomial. Incompressibility is taken into account by means of the Lagrange multiplier—in the form of mean hydrostatic pressure determined within each finite element. Particular attention was paid to the directional properties of cord ply treated as monotropic linear-elastic material characterized by effective material constants. These properties were introduced into the model by overlaying the elements with monotropic material on those representing rubber. The total Lagrangian description with the Green–Lagrange strain tensor and the energetically conjugate to it the second Piola–Kirchhoff stress tensor were applied to the tyre model. The results of a truck tyre analysis concerning displacements and delamination stresses distribution show good accuracy of the pneumatic tyre modelling technique proposed in the paper.