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Maik Brehm, Thierry J. Massart, Arnaud Deraemaeker

Keywords dynamic response simulation, implicit gradient damage law, model calibration, optimisation, sensitivity analysis, uncertainty propagation


Prof Michel Coret, Ecole Centrale Nantes, France

Prof J. Réthoré, INSA Lyon, France



The development of new and the improvement of existing damage indicators applicable in Structural Health Monitoring require reliable test data for various damage states of the structure. Such experiments are usually very expensive in terms of material and labour costs. Therefore, a growing interest exists in replacing expensive experiments at least partly by virtual tests. Especially for concrete structures, such tests are expensive as several tests are required to consider the high variability of material parameters.

For damage indicators based on local measurements, such as strains, a realistic local representation of the damage is of high importance. Damage progress models based on an implicit gradient damage approach are suitable models to represent concrete cracking. However, deficits are still existing in defining realistic material and damage law parameters. Besides a realistic damage pattern, an efficient methodology to simulate the dynamic vibrations is needed, especially if the statistics of the response values under random excitation is of interest.

This research topic combines the fields of fracture mechanics and structural dynamics. In addition, advanced strategies of sensitivity analysis, optimisation, and uncertainty propagation are indispensable.

damage progress beam

Figure 1: Simulation of cracking for a beam under three-point bending test.
(left: damage progress; right: load-deflection curve)


Dynamic responses under random excitation

With larger systems and the increase of degrees-of-freedom, time integration can be computationally very expensive. Especially, if the material parameter variability needs to be investigated under random excitations. To overcome this problem, an innovative quasi analytical approach in the frequency domain is proposed which reduces the computation time to about 2% in comparison to straightforward methods [2,5]. Nevertheless, this method is only applicable under the assumption of neglecting nonlinear effects, such as, from crack breathing. The implementation of crack breathing is one of the  current research interest.

Virtual testing scheme

Figure 2: General scheme of virtual testing using random loading in time and space.


Calibration of material and damage law parameters

To obtain a most realistic model of the damaged structure, uncertain parameters of a suitable damage law should be determined. This can be realised by a fitting of numerically derived and experimentally obtained results using  nature-inspired optimisation algorithms (e.g., Covariance Matrix Adaptation Evolution Strategy). Important for a successful calibration are the consideration of measurement uncertainties and remaining uncertainties of the determined parameters [3]. In the focus of current research is the design of experiments to determine uniquely the parameters of an implicit gradient damage law (e.g., image correlation).

Three point bending test      Dynamlic response

Figure 3: Left: experimental test setup in the laboratory;
Right: comparison initial and updated load-deflection-curve.


Simplification of damage pattern


However, advanced damage propagation models are computationally very expensive and are only applicable for a limited number of structures. Moreover, such approaches are so far hardly available for full 3D models. This is essential for the design of SHM systems of bridges, for example. Hence, a simplified representation of the damage is requested. Therefore, the possibilities of replacing expensive numerical continuum damage models by linear elastic models has been investigated [1].

damage patterns

Figure 4: Comparison of distribution of the Young's modulus for different damage models.



2011-2013: FNRS-MIS: Dynamic Strain Sensing for Structural Health Monitoring

Selected publications

[1] M. Brehm, T.J. Massart and A. Deraemaeker. Modeling of concrete cracking for the design of SHM systems: comparison of implicit gradient damage models and simplified linear representations. In Proceedings of 8th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS), March 10-14, Toledo, Spain, 2013.

[2] M. Brehm, T.J. Massart and A. Deraemaeker. Application of an updated notched beam model using an implicit gradient cracking approach for the purpose of damage detection based on dynamic strains. In Proceedings of ISMA conference on Noise and Vibration Engineering, September 17-19, Leuven, Belgium, 2012.

[3] M. Brehm, T.J. Massart and A. Deraemaeker. Towards a more realistic representation of concrete cracking for the design of SHM systems: updating and uncertainty evaluation of implicit gradient cracking models. In Proceedings of 6th European Workshop on Structural Health Monitoring, July 3-6, Dresden, Germany, 2012.

[4] A. Deraemaeker. Assessment of damage localization based on spatial filters using numerical crack propagation models. In Proceedings of 9th International Conference on Damage Assessment of Structures (DAMAS), July 2011, Oxford, UK, 2011.

[5] M. Brehm and A. Deraemaeker. Uncertainty quantification of dynamic responses in the frequency domain in the context of virtual testing. Journal of Sound and Vibration, 342:303–329, 2015.