M. Dittmann

Isogeometric analysis and hierarchical refinement for multi-field contact problems

The present work deals with multi-field contact problems in the context of IGA. In particular, a thermomechanical as well as a fracture mechanical system is considered, where novel formulations are introduced for both. The corresponding discrete contact formulations are based on a variationally consistent mortar approach adapted for NURBS discretized and hierarchical refined surfaces. Finally, the capabilities of the proposed framework are demonstrated within numerous numerical examples.

A higher order phase-field approach to fracture for finite-deformation contact problems

The present contribution provides a comprehensive computational framework for large deformational contact and phase-fracture analysis and is based on the recently appeared publication [16]. A phase-field approach to fracture allows for the efficient numerical treatment of complex fracture patterns for three dimensional problems. Recently, the fracture phase-field approach has been extended to finite deformations (see [18] for more details). In a nutshell, the phase-field approach relies on a regularization of the sharp (fracture-) interface. Besides a second-order Allen-Cahn phase-field model, a more accurate fourth-order Cahn-Hilliard phase-field model is considered as regularization functional. For the former standard finite element analysis (FEA) is sufficient. The latter requires global C continuity (see [3]), for which we provide a suitable isogeometric analysis (IGA) framework. Furthermore, to account for different local physical phenomena, like the contact zone, the fracture region or stress peak areas, a newly developed hierarchical refinement scheme is employed (see [19] for more details). For the numerical treatment of the contact boundaries we use the variational consistent Mortar method. The Mortar method passes the patch-test and is known to be the most accurate numerical contact method. It can be extended, in a straightforward manner, to transient phasefield fracture problems. The performance of the proposed methods will be examined in several representative numerical examples.