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    Die Kriminalprognose und das Risiko

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    A THREE-INVARIANT, EXPERIMENTAL BASED, ELASTOPLASTIC FORMULATION FOR STEEL MATERIALS

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    The pressure sensitivity of metals is addressed in this work. A series of experimental tests, considering different load scenarios able to activate non- deviatoric stress tensor invariants, were performed on steel solid round bars [1, 2]. The load was applied to the specimens in the form of uniaxial tension/compression and torsion combinations which will result in combined tensile and shear stresses that will maintain a constant ratio during the experiment. A digital image correlation system was used to monitor the experiments and provide the displacement field and the strain field distribution at different stages of the tests. This photogrammetric non-contact device was mounted in front of the painted sample, for continuous recording of the relative movement of black dots on the white specimen during the deformation. 3D analyses were carried out and the need to expand the von Mises elastoplastic constitutive model, with an associated flow rule, to a formulation that takes into consideration also the first invariant of the stress tensor and the third invariant of the deviatoric stress tensor was highlighted; so reproducing the main features of the experimental results. A more sophisticated hardening law was proposed as a function of three invariants of the plastic strain tensor. Plastic flow rule was derived by integration of the plastic strain rate through the physical domain of the specimen (elaboration of DIC results) and expressed in terms of the three invariant formulation of the stress tensor to activate the proposed hardening law

    Tree size mostly drives the variation of xylem traits at the treeline ecotone

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    Key message: The axial structure of the hydraulic system in trees is relatively invariant and insensitive to temperature, while trees plastically adjust the number of cells within the tree ring. Abstract: At higher elevations and latitudes in the treeline ecotone, reduction in the heat accrued during the growing season is reflected in gradually decreasing tree size. Due to low temperatures, treeline trees might produce smaller xylem cells and, as a consequence, tree growth could be limited. However, some xylem traits (i.e., cell lumen area) are considered relatively insensitive to climatic factors but highly dependent on tree size because of the natural widening of xylem conduits towards the stem base. We tested the hypothesis that earlywood cell lumen area is essentially invariant and depends largely on tree size. Tracheid traits in four conifer species from the lower (“timberline”) and upper (“treeline”) parts of the treeline ecotone (Picea engelmannii, Picea abies, Pinus cembra and Larix decidua) were measured in the Colorado Front Range (U.S.A.), Krkonoše Mts. (Czech Republic) and Dolomites (Italy). On transversal sections sampled at 1 m of stem height, we measured cell lumen areas, transversal cell size, cell wall thickness, tree-ring width and number of cells per radial file. Cell lumen areas were always greater at the timberline than treeline. When tree height is accounted for, the earlywood cell area did not differ between the two sites, thus showing that difference in temperature did not affect earlywood cell area in any of the four measured species. The number of cells within tree rings exhibited high inter-annual variability according to environmental factors. The fundamental hydraulic structure in trees is relatively rigid and insensitive to temperature, while trees plastically adjust the number of cells within the tree ring as a result of inter-annual climate variability and leaf production
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