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The reliable numerical simulation of the initiation and propagation of cracks plays an important role for the integrity assessment of concrete structures. To this end a large number of material models for concrete cracking based on different theories (e.g., damage mechanics, fracture mechanics, plasticity theory and combinations of the mentioned theories) as well as advanced finite element methods suitable for the representation of cracks (e.g. the Extended Finite Element Method and Embedded Crack Models) have been developed in recent years.
Classical models for concrete cracking are based either on the so-called smeared crack approach or the discrete crack approach. Smeared crack models are based on the theory of continuum mechanics and are characterized by spreading the dissipated energy along the width of the localization band. The class of discrete crack models is characterized by incorporating the discontinuity of the displacement field due to cracking directly into the finite element formulation in order to capture the strong discontinuity kinematics of a discrete crack. To this end, a discontinuity interface is introduced. Its behaviour is described by a discrete traction-separation law. In contrast to crack faces introduced along element boundaries, the strong discontinuity kinematics can be introduced within the domain of a finite element. Hence, a macroscopic crack path may cross a given spatial discretization in an arbitrary way. In this context one can distinguish between enriching elements with additional degrees of freedom, representing the displacement jump across the crack, and enriching nodes with additional degrees of freedom. The former method is denoted as elements with embedded discontinuities, whereas the latter is known as the Extended Finite Element Method.
The aim of this CISM Course is to impart basic knowledge of the different approaches for modelling damage and cracking of concrete and to provide a critical survey of the state-of-the-art in this field of computational mechanics. The lectures cover a relatively broad spectrum of topics related to crack modelling, including continuum-based and discrete crack models, induced anisotropy, advanced crack models based on the concept of finite elements with embedded discontinuities and on the extended finite element method, models of crack propagation in concrete subjected to cyclic and dynamic loading and meso-scale models for cracked concrete. Also, extensions to coupled problems such as hygro-mechanical problems will be addressed. Special emphasis will be put on the potentials of the different approaches for practical applications in Civil Engineering.
The course is addressed to doctoral students, young researchers and practicing engineers.
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