NONLINEAR ANALYSIS OF TEXTILE REINFORCED CONCRETE SHELLS USING AN ANISOTROPIC, DAMAGED-BASED MATERIAL MODEL

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1 NONLINEAR ANALYSIS OF TEXTILE REINFORCED CONCRETE SHELLS USING AN ANISOTROPIC, DAMAGED-BASED MATERIAL MODEL Ehsan Sharei (1), Alexander Scholzen (1), Rostislav Chudoba (1), (1) Institute of Structural Concrete, RWTH Aachen University Abstract: Thin shell structures made of Textile Reinforced Concrete (TRC) exhibit a physically nonlinear response due to the strain-hardening behavior of the composite. For the simulation of thin walled TRC structures, an anisotropic damage-based material model of a microplane type has been used to reflect the propagation of fine, oriented cracks during the loading. In this paper a method for calibration and validation of a TRC cross section is proposed and demonstrated. After providing a brief summary of key assumptions of the material behavior, the calibration procedure using tensile test data is presented. Then the model is validated by simulation of a test on a TRC vault shell. The comparison is performed both for the load-displacement response and for the observed and calculated distributions of cracks. Finally, the feasibility and validity of the computational model is discussed. INTRODUCTION Textile Reinforced Concrete (TRC) can fulfill the demands of innovative structural designs by offering a high load bearing capacity and durability. A TRC cross section consists of fine-grained concrete layers and reinforcing layers of carbon or glass fabrics. Due to the non-corrosive reinforcement thin cross sections with a thickness of only a few centimeters can be realized. The textile reinforcement has a high form flexibility that enables also the construction of lightweight shell structures with curved shapes [1,2]. Its material characteristics make the composite material also highly attractive for various other fields of application such as ventilated facade elements or sandwich panels with TRC facings [3]. TRC as an inhomogeneous composite material exhibits an anisotropic crack formation which depends on the direction of the principle stress in a shell structure. Except of this damage-induced anisotropy, initial anisotropy due to the orientation of the fabrics can be observed as well. The tensile stress-strain response of the composite material exhibits a pronounced strain-hardening effect. In order to cover the anisotropic and nonlinear behavior of TRC, an anisotropic damage model of microplane type with smeared representation of finely distributed matrix cracks has been used in this paper. The model is based on the microplane damage model described in [4] and [5] that has been utilized for the application to TRC shells [6]. Figure 1 shows a procedure of calibration and validation of the model. On the left hand side a typical damage function is shown. This function determines the evolution of damage based on the direction of loading and is identified by an iterative calibration procedure which is described in [7]. Using this function, the experimental stress-strain curve from a 133

2 tensile test can be fully reproduced in the numerical simulation. The model has been validated by comparing the prediction with the TRC bending tests and slab tests with the same cross-sectional thickness and reinforcement ratio (Figure 1, right). In the present paper the ability of the anisotropic damage model to reproduce complex stress states within TRC shell structures is investigated using a large scale test of a TRC barrel-vault shell. The material model is implemented as a user subroutine for 4-node bilinear isoparametric finite shell elements with reduced integration in the commercial finite element software ABAQUS [8]. This implementation corresponds to a former implementation of the model for solid shell elements [9]. Figure 1: Schematic description of the procedure for calibration and validation of the nonlinear computational model The aim of this paper is to demonstrate the feasibility of the model in simulation of complex TRC shell structures. The capability of the model is discussed in terms of its ability to predict the crack formation and to estimate the load bearing capacity of the shell structure. CALIBRATION OF DAMAGE FUNCTION USING A TRC TENSILE TEST In order to calibrate the material model for TRC, a series of uniaxial tensile tests has been performed. Figure 2 right shows the TRC specimen with six layers of textile reinforcement made of carbon bonded with the fine-grained concrete matrix. Dimensions of the specimen are shown in Figure 2 left. Strain is measured by displacement gauges on both side of the specimen with a measuring length of 25 cm. 134

3 Figure 2: Geometry of tensile test specimen and position of the displacement gauges (left); cross-sectional layout with six layers of carbon textile fabrics (right) Figure 3: Damage function calibrated for the tensile test of TRC specimen (left) and stress-strain curves of tensile test corresponding to experiment and simulation (right) Figure 3 (left) shows the calibrated damage function with elasticity modulus E = MPa and Poisson s ratio ν = 0.2. The simulation of the tensile test shown in Figure 3 (right) performed with the calibrated damage function, showing the match between the stress-strain curves from the test and from the simulation. VALIDATION OF THE MODEL USING A TRC VAULT SHELL The TRC barrel-vault shell shown in Figure 4 was fabricated with the cross-sectional layout corresponding to Figure 2 (right) 135

4 Figure 4: Dimensions of the tested and simulated TRC barrel-vault shell The thickness of the shell was 2 cm containing 6 layers of equidistantly placed fabric layers of carbon. The shell was placed on four steel supports providing a radial and tangential constraint at each support. This structure was tested under a radial loading applied by means of a steel stripe which was pulled using a hydraulic cylinder on each side as shown in Figure 5. Two different types of supports have been used during a loading-unloading-reloading scenario. At the first loading step up to a force of F = 60 kn in the hydraulic cylinders, the radial displacement was allowed at the supports. After that, the shell was unloaded and the radial displacements were fixed by means of screwed bolts in order to prevent uplifting of the shell during the test. With the fixed radial displacements the shell was reloaded up to the failure load (Figure 6). 136

5 Figure 5: Test setup for the measurement of the load bearing capacity of the investigated TRC barrel-vault shell (up), tested prototype in the laboratory (down left) and detail of load introduction via hydraulic cylinders (down right) The chosen loading scenario led to finely distributed crack pattern throughout large zones of the shell as intended by the design of the test setup. The highest tensile stresses developed along the shell edges in the longitudinal direction where also the ultimate failure of the shell occurred. The ultimate breaking strain of the composite in these regions was measured using two displacement gauges as shown in Figure 5 (top). The numerically obtained damage of the shell at the ultimate load is shown in Figure 6. In agreement to the experiment, largest values of the damage indicator occur in the middle of the longitudinal shell edges. Moreover, due to the chosen loading and boundary conditions the structure was also exhibiting damage zones at the front and at the back side of the structure. Also this result agrees well with the observation in the test and documents the ability of the model to reproduce the matrix fragmentation process within a complex structural geometry and boundary conditions. 137

6 Figure 6: Damage contour in the TRC vault shell under load F and the loading-unloading path with the corresponding change in the support conditions Figure 7: Load-tensile strain curve from the simulation of the TRC barrel-vault shell compared to the experimental results for the left and right side of the shell (unloading branch is not shown) A qualitative comparison between test and simulation is provided in Figure 7 showing the load F and the corresponding strain measured by the two displacement gauges at the longitudinal edges of the shell is plotted in Figure 7. The applied loading history is sketched in the diagram in Figure 6 containing the loading, unloading and reloading branches. The calculated prediction slightly underestimates the measured response as shown in Figure 7. Obviously, the test results are not perfectly symmetric. Further improvements and detailing of the numerical model including the sensitivity of the response with respect to the slight perturbations with respect to the geometry will be 138

7 included in the next phase of analysis. Yet, the shown results demonstrate the ability of the model to capture the trend of the strong nonlinear structural response for the described loading-unloading-reloading scenario. SUMMARY In this paper a calibration of an anisotropic damage model for the simulation of TRC shell structures with a given material properties, cross-section and textile fabric reinforcement is presented. This model is based on microplane damage model and cares for the anisotropy and physical nonlinearity of textile reinforced concrete. After the calibration step, model was validated by simulation of a test on a TRC vault shell. The model has shown a good suitability in representation of fine and discrete cracks. Results from the simulation show also a good correspondence to the experimental results in the estimation of load bearing capacity. ACKNOWLEDGMENT The financial support of the German Research Foundation (DFG) within DFG project CH 276/2-2 is gratefully acknowledged. REFERENCES 1. A. Scholzen, R. Chudoba, J. Hegger. Thin-walled shell structure made of textile reinforced concrete; Part I: structural design and construction. Structural Concrete, 16(1), 2015, DOI: /suco (in press). 2. A. Scholzen, R. Chudoba, J. Hegger. Thin-walled shell structure made of textile reinforced concrete; Part II: experimental characterization, ultimate limit state assessment and numerical simulation. Structural Concrete, 16(1), 2015, DOI: /suco (in press) 3. A. Shams, M. Horstmann, J. Hegger. Experimental investigations on textile-reinforced concrete (TRC) sandwich sections. Composite Structures, Vol. 118, pp , December I. Carol and Z. P. Bažant. Damage and plasticity in microplane theory. International Journal of Solids and Structures, 34(29), pp , M. Jirásek. Comments on microplane theory. Mechanics of Quasibrittle Materials and Structures, Hermes Science Publications, pages 55-77, E. Sharei, A. Scholzen, R. Chudoba and J. Hegger. Anisotropic Damage Model for the Numerical Simulation of Textile Reinforced Concrete Shell Structures", The Twelfth International Conference on Computational Structures Technology, B.H.V. Topping and P. Iványi, (Editors), Civil- Comp Press, Stirlingshire, United Kingdom, paper 9, R. Chudoba and A. Scholzen. Modeling of reinforced cementitious composites using the microplane damage model in combination with the stochastic cracking theory. Proceedings of EURO-C 2010, Rohrmoos/Schladming, Austria, March ABAQUS User Subroutines Reference Manual, Version 6.11, Dassault Systèmes Simulia Corp., Providence, RI, USA, A. Scholzen, R. Chudoba, J. Hegger, Calibration and validation of a Microplane damage model for cement-based composite applied to Textile Reinforced Concrete, International Conference on Recent Advances in Nonlinear Models - Structural Concrete Applications, H. Barros, R. Faria and C. Ferreira (Editors), pp ,

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