Dr.-Ing. Sven Reinstädler
Residual load capacity of damaged steel structures
During earthquakes structures may experience high loads. A decision regarding a restoration and further usage of a damaged structure can be taken a lot easier, when residual load capacities of their supporting components are stated by numerical analysis. A realistic numerical analysis is possible, if appropriate mathematical models describe both, the time-varying loading during earthquakes and the inelastic deformation behavior of steel. Kowalsky [1] and Zümendorf [2] describe the inelastic behavior of steel with a model for ductile damage. In figure 1 evolutions of selected state variables are shown for cyclic increasing strain.
Figure1:
Evolution of state variables for cyclic increasing strain
The paths of isotropic and kinematic hardening show, that the yield stress is already exceeded during the first load cycle. Furthermore the steady state with alternating kinematic hardening is reached after a few cycles. The material model takes into account that damage evolutes only during tensile loading when a critical ultimate strain is exceeded. Therefore and due to the low viscosity of steel the damage increases suddenly in several steps until the material is incapable to carry any stress. The work equation
describes the deformation behavior of flexible structures in space and time [3]. It is transferred into a finite element formulation [4] and used for models by which the deformation behavior of steel structures can be studied even in case of accelerations during earthquakes. In figure 2 a bulged steel beam is shown, whose ends are shifted relatively to each other. The damage of a fictitious tie bar in the longitudinal direction of the bulge falling in is clearly visible.
Figure2:
State variables along a bulged steel beam
Although the stability of thin-walled steel beams can be investigated, small strains are assumed using the strain balance equation above. The aim of the research project is to develop a continuum mechanical model allowing for large strains during ductile damage. The model will be used to investigate the residual load capacity of damaged steel structures where large strains are expected due to the impact of earthquakes.
Publications within the framework of the RTG:
Publications in peer-reviewed scientific journals:
S. Reinstädler, U. Kowalskya and D. Dinkler. Analysis of landslides employing a space-time single-phase level-set method, Computer Methods in Applied Mechanics and Engineering 347, S. 639-662, 2019.
E. Adeli, B. Rosić, H.G. Matthies and S. Reinstädler. Effect of Load Path on Parameter Identification for Plasticity Models using Bayesian Methods. QUIET, 2018.
E. Adeli, H.G. Matthies, S. Reinstädler and D. Dinkler. Comparison of Bayesian Methods on Parameter Identification for a Viscoplastic Model with Damage. DOI: 10.13140/RG.2.2.30280.26889, 2019.
E. Adeli, H.G. Matthies, S. Reinstädler and D. Dinkler. Bayesian Parameter Determination of a CT-Test described by a Viscoplastic-Damage Model considering the Model Error. DOI: 10.13140/RG.2.2.26924.82562, 2019.
Conference contribution with publication in conference proceedings:
E. Adeli, B. Rosić, H.G. Matthies and S. Reinstädler. Bayesian Parameter Identification in Plasticity. XIV International Conference on Computational Plasticity, COMPLAS 2017.
Additional literature:
U. Kowalsky, J. Meyer, S. Heinrich and D. Dinkler. A nonlocal damage model for mild steel under inelastic cyclic straining. Computational Materials Science, 63:28-34, 2012.
T. Zümendorf. Ein gradientenabhängiges Modell für Schädigung bei viskoplastischem Materialverhalten. Dissertation, TU Braunschweig, 2006.
T. Hughes and G. Hulbert. Space-time finite element method for elastodynamics: Formulations and error estimates. Computer Methods in Applied Mechanics and Engineering, 66:339-363, 1988.
S. Reinstädler. Modellbildung und numerische Analyse der Entleerung von dünnwandigen Silos. Dissertation, TU Braunschweig, 2016.