An efficient PODI method for real-time simulation of indenter contact problems using RBF interpolation and contact domain decomposition

This paper proposes an efficient proper orthogonal decomposition with interpolation (PODI) method for real-time simulation of indenter contact problems. In the offline stage, POD models are constructed from displacement and von-Mises stress snapshots of full-order finite element solutions of indenter contact problems with training contact locations and indentation depths. Indentation depth and contact location are respectively used to interpolate POD basis vectors and POD coefficients by Lagrange interpolation with a congruence transformation and radial basis function (RBF) interpolation. In the online stage, displacements and von-Mises stress of solids under a new indentation loading are obtained very quickly by using the interpolated POD matrix and POD coefficients. A clustering-based contact domain decomposition (CDD) scheme is proposed to further improve the computational performance of the present PODI–RBF​ method. Numerical results show that the PODI–RBF method using the CDD scheme can be used to obtain finite element solutions of indenter contact problems at 400 ∼900 Hz on a personal computer for finite element models with 8000 ∼16000 nodes, which is promising to real-time simulation of indenter contact problems.