Cracks play a major role for the determination of a structure's safety. Fracture mechanics describes the mechanical behavior of cracked bodies and provides models for crack growth. The simulation of crack propagation is a great challenge for simulation methods. In classical finite element analyses, meshes have to be used which are decoupled along the crack path and are refined near the crack tips. However, the crack path is part of the solution and not known beforehand, so that meshes have to be successively updated during the propagation. The automatic generation of suitable meshes is a difficult task, especially in three spatial dimensions. At the Institute of Structural Analysis, the extended finite element method (XFEM) is used for simulations of crack propagation in two and three dimensions. The advantage of the method is that simple, fixed meshes can be employed which are independent of the advancing crack. The crack is considered by an extension of the approximation space of the classical FEM.

Bio mechanics heavily promoted the developent of new and advanced models in continuum mechanics in the last decade. Typically, they are classified as multi-physics or multi-field applications and require sophisticated numerical methods for the simulation. In the context of bio mechanics, the Institute of Structural Analysis focusses on bone fracture and fluid-structure interaction.

In the context of plasticity and large deformations, the research at the Institute of Structural Analysisis is also concerned with non-linear models and advanced finite element technology. Our aim is to improve the simulation of existing models rather than the development of new (material) models. For example, the proper consideration of the interface between the elastic and plastic zones inside a domain of interest is addressed. Other topics are mesh refinements (*h*-FEM), FEM with higher-order accuracy (*p*-FEM), iterative solvers and preconditioning, shell elements, mixed and hybrid elements, enhanced-assumed-strain elements and reduced-order integration.

The incompressible and immiscible flow of two fluids with different properties such as viscosity and density is of importance in many technical applications. At the dynamically moving interfaces, jumps and kinks (i.e., discontinuities) are present in the physical fields such as velocity and pressure. These instationary discontinuities have to be properly treated in the numerical methods for the simulation. Typical applications include tank sloshing, collapsing water columns, dam breaks, and bubble flows.

One approach to consider the dynamic interface is to frequently update the mesh such that the element edges * track the interface*. However, for large movements of the interface including topological changes of the two fluid regions, mesh adaptions are virtually impossible. Another approach is to use fixed background meshes and

Free-surface flows can also be seen as a special case of two-phase flows where one phase ("air") has neglible influence on the other ("water"). The location of the interface is not known beforehand and is part of the solution. At the Institute of Structural Analysis, the overflow of objects, flow in spill-ways of dams and the impact on wave breakers have been succesfully simulated in two and three dimensions.

The interaction of a fluid with a deforming structure is an important problem in structural dynamics. The famous example of the Tacoma-Narrows bridge, which collapsed under the resonant reaction of the bridge with a moderate wind flow, demonstrates the possible consequences of this interaction and its importance in the safety of structures. The simulation of this coupled problem in two and three dimensions is an important application at the Institute of Structral Analysis.

Tunneling plays a major role in Austria due to its geological characteristics. The understanding of the mechanical behavior during the excavation and the quantification of deformations and stresses in the surrounding rock are important for the safety. In general, the domain around a tunnel is considered to be infinite. Hence, the BEM is particularly useful since it does not rely on a domain discretization and beyond it fulfills the radiation condition explicitly. Special techniques enable the treatment of non-linear material models, non-homogeneous domains, ground support, and sequential construction in the context of the BEM.

Fracking is the injection of a fluid into a reservoir under high pressure. The aim is to improve the permeability of the reservoir by inducing fractures and thereby enhance the productivity. This treatment is routinely applied in oil and gas reservoirs and, more recently, also in geothermal reservoirs. For the simulation, the fluid model is coupled to the crack propagation model. At the Institute of Structural Analysis, the focus is on an arbitrary, i.e. unconstrained, propagation of the crack surface in two and three dimensions using a simplified fluid model. The application is in geothermal reservoirs, in particular using the hot-dry-rock method.