Abstract

This project aims at introducing a new discretization method for contact of bulky and thin-walled structures exhibiting pronounced geometrical and material nonlinearities. The resulting smooth contact approach will go beyond traditional smoothing procedures with regard to a sound mathematical basis, but will at the same time retain the simplicity of low-order finite element discretizations in the bulk of the computational domain. Volume and contact surface discretizations are strictly separated, but interconnected via variationally consistent coupling operators based on generic biorthogonal Lagrange multiplier bases. This new approach promises to offer maximal flexibility with regard to a smooth surface discretization (e.g. using higher-order FE, Hermite interpolation, splines or NURBS) and a completely independent volume discretization (e.g. using low-order non-conforming FE, EAS or F-Bar techniques).

In addition, an integrated treatment of contact and friction as well as finite strain plasticity based on so-called nonlinear complementarity functions and semi-smooth Newton methods will be developed,  which possibly offers a superior robustness as compared with traditional radial return mapping  schemes. Both proposed topics on their own, and especially their combined numerical treatment, are anticipated to allow for significant progress towards truly reliable simulation techniques for complex problem scenarios in nonlinear solid and structural mechanics.