Application of a-priori hyper-reduction to the nonlinear dynamic finite element simulation of a rolling car tire

The a-priori Multi-Expansion Modal (MEM) hyper-reduction method for nonlinear structural dynamics finite element problems is described, extended and applied to the dynamic nonlinear finite element simulation of a car tire rolling over a rough road surface, including geometrical, material, follower force and contact nonlinearities. Rather than using time-domain training simulation data, a-priori calculated static nonlinear contact configurations and eigenmodes are used as a reduction basis and to perform the hyper-reduction element sampling. The hyper-reduction element sampling is performed by solving an L1 optimization problem subject to a set of equality constraints. This yields a reduced set of elements with an a-priori known cardinality, which depends on the amount of constraints taken into consideration and the reduction basis dimension. It is shown that care has to be taken during the hyper-reduction process when considering distributed contact constraints, as is the case for e.g. a tire rolling over a rough road surface. Large speedup factors can be obtained while still retaining a relatively high accuracy, making application of the MEM method suitable to for instance industrial design optimization cases.status: publishe