Computational Structures Technology
Chapter 14 Y.S. Petryna+, W.B. Krätzig* and F. Stangenberg+
+Institute for Reinforced and Prestressed Concrete Structures *Institute for Statics and Dynamics Ruhr-Universität, Bochum, Germany Keywords: material damage, simulation, reinforced concrete structures, damage measure, statistical uncertainties. This paper deals with two actual issues of computational structures technology - simulation and assessment of structural damage. The paper shows how the understanding of damage processes helps to define, quantify and even to measure the damage degree of structures. Damage simulation begins usually with a proper nonlinear material modeling able to describe deformation processes with damage constituents. Among a wide variety of damage phenomena the present work concentrates on mechanical damage of reinforced concrete under monotonic and cyclic loading. From the simulation viewpoint the so-called instantaneous (time-independent) and essentially long-term damage effects are distinguished. The plasticity and micro-cracking of concrete under compression, the fracture of concrete under tension, the yielding of reinforcement and the damage of the bond between concrete and steel under static loading belong to the first group. The paper discuss main features of a uniform material model of reinforced concrete able to simulate these processes and refer to such a model recently developed in [1]. The model is based on elasto-plastic continuum damage theory and implemented in the finite element software FEMAS [2]. This material model is further extended to account for such long-term damage effects as high-cycle fatigue and creep, relevant to many practical problems of civil engineering structures. In contrast to existing models the new fatigue damage model proposed in [3] accounts for damage evolution, for impact of fatigue on system behavior as well as its feedback. Therefore, it is able to realistically predict intermediate material states during fatigue life. The damage evolution law for concrete is adopted in accordance to the history of plastic strain accumulation observed experimentally and then calibrated on the fatigue life predictions resulting from the S-N (Wöhler) curves. For damage accumulation in steel, acceptable estimates are obtained using the Palmgren-Miner hypothesis. The concrete creep is described by the rate-type law and the non-aging rheologic model according to the solidification theory [4]. As only long-term consequences of creep are of interest, the relevant creep strain is reduced to the so-called visco-elastic strain. The creep law is integrated over time by the unconditionally stable exponential algorithm using the middle point of each time interval in the logarithmic scale. The interaction of time-independent and long-term damage mechanisms takes place during the equilibrium iterations of the finite element structural model. Several approaches have been developed in the last decades to evaluate structural damage through changes in dynamic response. However, they are typically limited to damage detection and localization. A basic concept of structural damage assessment with respect to carrying capacity, a challenging task of any assessment, has been recently proposed by the first two authors [5]. The present contribution completes this approach with a new virtual-energy-based (VEB) structural damage measure estimating reduction of the strain energy attributed to vibration modes. The VEB damage indicator has been shown to be closely related to the Mode Assurance Criterion (MAC) widely used in vibration monitoring. This fact opens the perspective of its successfully application both in numerical and experimental assessment techniques. The inherent uncertainties of material, geometrical and structural parameters are taken into account statistically. The finite element structural analysis is combined with Monte-Carlo simulations to solve the eigenvalue problem with respect to randomly generated stiffness and mass matrices and determine the output statistics of the damage measure. For illustration purposes the approach has been applied first to simulate and then to estimate the damage evolution of a reinforced concrete beam. The results obtained numerically are compared to experimental ones available in the literature. The sensitivity of modal parameters and damage measures to uncertainties are statistically studied in the second example of a 3-span slab concrete bridge. References
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