Journal Article10.1061/JMCEA3.0002347
Closure to “Instability, Ductility, and Size Effect in Strain-Softening Concrete”
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TL;DR: In this article, structural instability due to strain-softening (i.e., declining branch of the stress-strain diagram) is presented, and the existence of a lower limit on the size of this region permits ductility, along with its dependence on the structure size and stored energy, to be predicted by a stability analysis.
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Abstract: Analysis of structural instability due to strain-softening (i.e., declining branch of the stress-strain diagram) is presented. In a continuum, strain-softening is impossible; it can exist only in a heterogeneous material. Failure occurs by unstable localization of strain or beam curvature, in which the stored strain energy of the structure is transferred into a small strain-softening region whose size is several times the aggregate size, or the spacing of reinforcement, or the depth of the beam. The existence of a lower limit on the size of this region permits ductility, along with its dependence on the size and stored energy, to be predicted by a stability analysis. Calculations of limit loads and moment redistributions in strain-softening beams and frames must include instability checks of possible curvature localization. The same applies to finite element analyses of reinforced concrete structures with account of tensile cracking, and predictions of limit loads of these structures which are questionable because they depend on the size of the finite elements.
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Citations
Modeling shear bands inJ2plasticity using a two-scale formulation via embedded strong discontinuity modes
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Shakedown with softening in reinforced concrete beams
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A microstructurally-based internal length for strain localization problems in dynamics.
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TL;DR: In this article, a two-scale dynamic damage law based on an intrinsic length at micro-scale, corresponding to the inter-distance between two adjacent micro-cracks, was proposed to regularize the strain localization problem in dynamics.
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Finite Element Model of Functionally-Graded Cementitious Panel under Small Projectile Impact:
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Probabilistic modeling of concrete structures
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