# Research at the Instute of Applied Mechanics

Solid mechanics and numerical analysis are the core research areas of the Institute of Applied Mechanics. The topics listed below are of particular interest. The Finite Element Method and the Boundary Element Method are used as numerical solution concepts.

# Numerical simulation of wave propagation

In many engineering applications, the simulation of waves in unbounded domains is required. In these multiphysical problems, several computational methods have to be used. The Boundary Element Method (BEM) in time-domain is the method of choice for the radiation of waves in the unbounded domain. These are examined and further developed at the institute. These advances are continuously incorporated into the in-house software HyENA (Hyperbolic and Elliptic Numerical Analysis). This software was also used to simulate the animations shown for elastodynamic wave propagation, which is caused by two inclusions in the full space under constant pressure.

# Acoustic behavior of poroelastic shells

The simulation of the acoustic behavior of poroelastic shells analyzes the sound transmission through thin porous structures. Related numerical methods have to address two aspects: one addresses the mechanical and acoustic response of the shell itself, while the other part deals with the coupling with the surrounding fluid (e.g., air). The simulation employs the Finite Element Method optimized for this particular application. The first figure illustrates the components of the problem: the soundhard boundary ∂Ω+, the interior fluid Ωint, the exterior fluid Ωext, and the shell Ωs. Below, we compare the computed sound pressure level at an internal point for elastic and poroelastic shells.

# Modeling and simulation of skeletal muscles

The aim of the modeling and simulation of skeletal muscles is to develop an innovative digital human model (manikin) with a detailed description of the skeletal muscles and fast numerical algorithms. We utilize a modeling approach based on mechanical multi-body systems (MBS) to capture the dynamics of the musculoskeletal system with sufficient accuracy. Such models stem from robotics and are already used in many biomechanical fields of application. The modeling of the musculature, however, is still an unresolved challenge. For this purpose, we develop a new one-dimensional continuum model that realistically describes individual muscle fiber bundles. This model shall replace conventional discrete force elements used in MBS models. Together with fast, problem-adapted numerical algorithms, it can be used for calculating movement sequences and for controlling the manikin.

# Modelling of porous materials

Porous materials can be found in nearly all engineering fields. In civil engineering well known examples are saturated or partial saturated soil, rock or concrete. The mostly used single-phase material models are not able to describe important effects. At the institute, two- or multi-phasic material modeles are under study including their respective realization in numerical simulation methods. Two actual projects are in the field of Biomechanics and the determination of waves in fresh concrete. In the first project, the growth of a thrombus in a dissected aorta is modeled with a poroelastic model. The phase change from blood to a solid material is the challenging part. In the second project, ultrasound measurements are simulated to determine the state of the material. For this a sound material model describing different phases within fresh concrete has to be developed. Further, the numerical realization is an important aspect to support this innovative measuring technique.

# Isogeometric boundary element method

Isogeometric methods employ the same functions (i.e., splines) used in CAD programs to describe objects for numerical simulations. These functions offer many computational advantages, such as high continuity.  Furthermore, isogeometric methods facilitate better interaction between CAD and simulation tools because the same model representation and data structures can be used. This aspect holds especially for isogeometric boundary element methods, since, like CAD models, they rely merely on the description of the boundary of an object. The figures show a simulation of the deformation of an elastic spanner, which was carried out directly on the CAD model.

# Higher-order beam and shell models

Beam and shell structures are of utmost importance for a wide range of applications. The mechanical behavior of such structures is described by beam- or shell-formulations, which employ certain assumptions to derive a mathematical model of the structures' physical properties. Regarding the numerical implementation of such formulations, our research focuses on higher-order approaches. In particular, methods based on level-set functions or isogeometric concepts are investigated.

The most common CAD models in engineering design are so-called trimmed geometries. At the same time, they are one of the biggest obstacles regarding the integration of CAD and simulation models. "Trimming" refers to a process used to show or hide regions of a CAD object. Hence, the actual geometry description of a model is usually much more complicated than its display in the CAD program (see figure). At the institute, we develop methods that allow the application of trimmed CAD geometries in numerical simulations. Thereby, two strategies are examined: one focuses on the treatment of trimming during the simulation, whereas the second strategy aims at deriving analysis-suitable representations of CAD models.