Christian Hesch

Energy-Momentum Conserving Schemes for Frictionless Dynamic Contact Problems

Dynamic contact problems in elasticity are treated within a finite element framework by employing the well-established node-to-segment method. A new formulation of the algorithmic forces of contact is proposed which makes possible the design of energymomentum conserving integrators. The numerical example presented herein indicates that the present approach provides enhanced numerical stability.

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.

MIXED INTEGRATORS FOR STRUCTURE-PRESERVING SIMULATIONS IN NONLINEAR STRUCTURAL DYNAMICS

Abstract. The present work deals with the design of structure-preserving numerical methods in the field of nonlinear elastodynamics and structural dynamics. Structurepreserving schemes such as energy-momentum consistent (EMC) methods are known to exhibit superior numerical stability and robustness. Most of the previously developed schemes are relying on a displacement-based variational formulation of the underlying mechanical model. In contrast to that we present a mixed variational framework for the systematic design of EMC schemes. The newly proposed mixed approach accomodates high-performance mixed finite elements such as the brick element due to Kasper & Taylor [15]. Accordingly, the proposed approach makes possible the structure-preserving extension to the dynamic regime of mixed high-performance elements. Numerical examples demonstrate the advantageous properties of the newly developed numerical methods resulting from the structure-preserving discretization in space and time.