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Existing design guidelines for concrete hinges are focusing on serviceability limit states. Lack of knowledge about ultimate limit states was the motivation for this work. Experimental data are taken from a testing series on reinforced concrete hinges subjected to eccentric compression up to their bearing capacity. These tests are simulated using the finite element (FE) software Atena science and a material model for concrete implemented therein. The first simulation is based on default input derived from measured values of Young's modulus and of the cube compressive strength of the concrete. The numerical results overestimate the initial stiffness and the bearing capacity of the tested concrete hinges. Therefore, it is concluded that concrete was damaged already before the tests. A multiscale model for tensile failure of concrete is used to correlate the preexisting damage to corresponding values of Young's modulus, the tensile strength, and the fracture energy of concrete. This allows for identifying the preexisting damage in the context of correlated structural sensitivity analyses, such that the simulated initial stiffness agrees well with experimental data. In order to simulate the bearing capacity adequately, the triaxial compressive strength of concrete is reduced to a level that is consistent with regulations according to Eurocode 2. Corresponding FE simulations suggest that the ductile structural failure of concrete hinges results from the ductile material failure of concrete at the surface of the compressed lateral notch. Finally, Eurocode-inspired interaction envelopes for concrete hinges subjected to compression and bending are derived. They agree well with the experimental data.

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Biological materials and systems are hierarchically organized.The main motivation for hierarchical biomechanics is that the wide variability of mechanical properties encountered at the macroscopic scale may be traced back to just a few universal. i.e. tissue-invariant, mechanical properties of elementary components at a sufficiently small scale (such as collagen, elastin, and water in case of soft tissues; complemented by hydroxyapatite in case of hard tissues), and to the nano and microstructures which the latter build up. This challenging task requires a physically rigorous and mathematically sound basis, as provided by Finite Element and Fast Fourier Transform methods, as well as by continuum micromechanics resting on (semi-)analytical solutions for Eshelby-type matrix-inclusion problems. Corresponding numerical and analytical mathematical models have undergone diligent experimental validation, by means of data stemming from a variety of biophysical, biochemical, and biomechanical testing methods, such as light and electron microscopy, ultrasonic testing and scanning acoustic microscopy, as well as physico-chemical tests associated with dehydration, demineralization, decollagenization, ashing, and weighing in air and fluid. While elastic scale transition and homogenization methods have attained a high maturity level, the hierarchical nature of dissipative (i.e. viscous or strength) properties is still a vibrant field of research. This applies even more to hierarchical approaches elucidating the interface between biological cells and extracellular matrices, and to the highly undiscovered mechanics unfolding within biological cells.

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