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Plain- and reinforced-concrete planar beam finite elements with embedded transversal cracking

In this work a primary fundamental ingredient of the mechanism – crack formation and development – is addressed and implemented in a planar layered reinforced-concrete beam element. The mechanism of crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the integration points reaching the tensile strength will trigger a crack to open. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle. A bond-slip relationship is superimposed onto this model in a kinematically coherent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in a multi-layered beam element. The discrete-crack embedded discontinuity approach is utilized in order to avoid the need for remeshing in smeared-crack model and artificial penalty stiffnesses in discrete-crack interface elements. The strain measures in a beam layer are related to the displacement and rotation functions using the geometrically exact Reissner’s beam model, which in the case of geometrically linear analysis reduces to the standard Timoshenko beam model.

fictitious crack model; layered beam element; embedded discontinuity; bi-linear damage

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