The life time performance of traditional fastening systems, as well as new future products, is determined by the performance of every single component and their interaction. Depending on the type of system, the base material can range from concrete or masonry to e.g. drywall. The anchor itself can be made from various metals or plastics and carry loads due to friction, shape interlock or adhesive glues. As shown in Figure both testing and simulation have to cover the behavior of single components, then their interaction and finally characterize the system behavior. This multi-scale problem can be numerically overcome by multi-scale modeling concepts, such as coarse graining or homogenization [1]. 

Over the years significant progress was made in accurately modeling single components based on extensive experimental investigations, see e.g. [2]. In addition to traditional continuum based elastic or elastic-plastic models, a broad range of continuum damage models as well as discrete models were developed, which mostly use a finite element or finite difference formulation. The former comprise crack-band models [3], non-local damage models [4, 5] but also microplane models [6, 7]. Typical examples for discrete models are e.g. lattice type particle models [8, 9].

Many studies were concerned with deterministic models to describe the load carrying capacity mostly under static short term loads. Similarly, modeling the component interaction was studied for certain problems. Modeling components under dynamic load on the other side was for some time neglected and only recently has become a focus of interest [10, 11]. Adequate stochastic models that can account for the true form of correlation between, and distribution of random variables are so far missing. In most research and codes simplifications are made by resorting to normally distributed variables and linear correlation, if at all considered. This approach unfortunately does not necessarily lie on the safe side and needs improvement.

Proposed solution and methodology As a first step a comprehensive mechanical modeling framework for single anchors will be built up. This has to describe and simulate the status of the system at short term loading. The main focus will be on concrete as base material; as a second priority masonry can be included as well. On the anchor system side mechanical and chemical systems will be captured. This includes on the material side the modeling of steel, adhesive resin and plastic elements and its interface conditions. First single components will be studied, followed by single fastening elements and later group configurations of anchoring points.

The CDL team and the Institute of Structural Engineering have extensive experience with concrete. Experience regarding the material characteristics of steel and mortars will be contributed by external collaborators.

The numerical simulations will be calibrated and verified by destructive tests of post-installed anchoring systems. Since the test configurations will be based on the numerical simulations, just tests for specific configurations and failure modes will be performed. It is planned to verify the numerical simulations for the different failure modes (pullout, breakout, splitting etc.), types of systems (mechanical, chemical, plastic etc.), base materials (concrete, masonry etc.) and loading conditions (static, dynamic, seismic etc.).

It should be emphasized that a combination of experiments with virtual testing is intended, utilizing efficient and reliable identification procedures of design - and assessment-relevant characteristics on basis of the developed multi-scale multi-phase modeling strategy. As a result, the number of tests needed for the characterization of a particular degradation mechanism or its effects on the life-cycle robustness of a particular type of fastening system can significantly be reduced compared to characterization approaches applying purely macroscopic, phenomenological models or that are based on empirical considerations only.

[1] J. Vorel, V. Šmilauer, and Z. Bittnar, “Multiscale simulations of concrete mechanical tests,” J. Comput. Appl. Math., vol. 236, no. 18, pp. 4882–4892, 2012.

[2] J. E. Hofmann, “Tragverhalten und Bemessung von Befestigungen unter beliebiger  uerbelastung in ungerissenem Beton,” Dissertation, Universität Stuttgart, Stuttgart, Germany, 2004.

[3] Z. P. Bažant and B. H. Oh, “Crack band theory for fracture of concrete.,” Matér. Constr., vol. 16, no. 3, pp. 155–177, 1983.

[4] Z. P. Bažant and G. Pijaudier-Cabot, “Nonlocal Continuum Damage, Localization Instability and Convergence,” J. Appl. Mech., vol. 55, pp. 287–290, 1988.

[5] G. Pijaudier-Cabot and Z. P. Bažant, “Nonlocal Damage Theory,” J. Eng. Mech., vol. 113, no. 10, pp. 1512–1533, 1987.

[6] J. Cervenka, Z. P. Bazant, and M. Wierer, “Equivalent localization element for crack band approach to mesh-sensitivity in microplane model,” Int. J. Numer. Methods Eng., vol. 62, no. 5, pp. 700–726, 2005.

[7] A. Beghini, Z. P. Bažant, Y. Zhou, O. Gouirand, and F. C. Caner, “Microplane model M5f for multiaxial behavior and fracture of fiber-reinforced concrete,” J. Eng. Mech., vol. 133, no. 1, pp. 66–75, 2007.

[8] G. Cusatis, D. Pelessone, and A. Mencarelli, “Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. I: Theory,” Cem. Concr. Compos., vol. 33, no. 9, pp. 881–890, 2011.

[9] G. Cusatis, A. Mencarelli, D. Pelessone, and J. Baylot, “Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. II: Calibration and validation,” Cem. Concr. Compos., vol. 33, no. 9, pp. 891–905, 2011.

[10] J. L. Le and J. Eliáš, “Numerical modeling of crack growth in quasibrittle structures under compressive fatigue,” presented at the 3rd International Conference on Life-Cycle Civil Engineering, IALCCE2012, Vienna, Austria, 2012, pp. 1296–1302.

[11] D. Pry, R. Pukl, and J. Cervenka, “Modeling high-cycle fatigue of Concrete specimens in three point bending,” presented at the 3rd International Conference on Life-Cycle Civil Engineering IALCCE 2012, Vienna, Austria, 2012, pp. 1303–1306.