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#### Organisationseinheit der BAM

The determination of material parameters from displacement field measurement is being examined for linear elastic solid. A frequently used approach to compute material constants can be found in many studies. Even though they presented the approach in many different variations, but in the end they are essentially based on the same algorithm: Parameters are iteratively tuned until the computed results are in accordance with the measurements. The main drawback of this approach is that mainly commercial software is used that hinders us to investigate its inner evaluation process. This leads to the question, how the results from this commercial software can be trusted. On the contrary to these debatable approaches, we present a method that inverts the procedure of finite element method by using the most general model for a least-squares adjustment – the GAUSS-HELMERT Model.

An energy-based method to determine material constants in nonlinear rheology with applications
(2016)

Many polymer-type materials show a rate-dependent and nonlinear rheological behavior. Such a response may be modeled by using a series of spring-dashpot systems. However, in order to cover different time scales the number of systems may become unreasonably large. A more appropriate treatment based on continuum mechanics will be presented herein. This approach uses representation theorems for deriving material equations and allows for a systematic increase in modeling complexity. Moreover, we propose an approach based on energy to determine thematerial parameters.This method results in a simple linear regression problemeven for highly nonlinearmaterial equations. Therefore, the inverse problem leads to a unique solution. The significance of the proposed method is that the stored and dissipated energies necessary for the procedure are measurable quantities. We apply the proposed method to a 'semi-solid' material and measure its material parameters by using a simple-shear rheometer.

Many engineering structures are made of composite materials or metal foam. To simulate the deformational behaviour of these structures often requires a high number of discretisation elements. This in turn yields a very large system of linear
equations that are extremely time and memory consuming or practically impossible to solve. It is therefore desirable to find an approach to overcome this obstacle.

The Measurement- and Model-based Structural Analysis (MeMoS) integrates a finite element model into least squares adjustment and thus allows to evaluate a mechanical model and measurements in a combined analysis. To examine the capability to detect and localise damage using this integrated analysis MeMoS, a small-scale truss bridge made of aluminium profiles is built as a test specimen for this purpose.

Within the presented research project, experimental and numerical investigations were performed to develop a thin-shelled, modular, mobile element system made of a micro-reinforced ultra-high-performance ductile concrete (DUCON®). Material parameters were experimentally determined to adapt the material model within the numerical analysis applying the Drucker-Prager relationship. Afterwards, for validation of the numerical models, quasi-static and high-velocity impact tests were performed on plate-like structures. Finally, a suitable geometry of transportable barrier elements will be designed, which provides a maximum of resistance against impact by a minimum of weight and a maximum of mobility.

To examine the capability to detect and localise damage using the Measurement- and Model-based Structural Analysis (MeMoS), a small-scale truss bridge (1520 mm × 720 mm × 720 mm) made of aluminium profiles is built as a test specimen for this purpose. The truss frame of the test bridge is made of aluminium profiles with a sophisticated design of the cross-sectional area. In comparison, with solid profiles, only a fraction of the material is needed to produce the profiles, while their bending resistance decreases slightly. The profiles are built into a truss frame by connecting them by means of fastening sets made of steel. The bridge model is mounted on four steel bearings which each of them consist of a cylinder arranged between two plates. Fixed bearings are made by holding onto one end of the bridge. The bridge is subjected by an external load by placing a heavy object beneath it. At the same time, measurements can be conducted below the bridge. Therefore, the bridge specimen is elevated by attaching it on a pedestal with four columns. Damages can be induced by loosening the fastening pieces.

The integration of finite element method (FEM) into the least-squares adjustment presented in is further extended for a joint evaluation of an elastostatic model and displacement field measurement. For linear solids which obey the Hooke's law, the material parameters determination from measurements is being examined.