FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elasto-plasticity and non-local softening

Korol, E. Z.; Tejchman, J.; Mróz, Z.

doi:10.1016/j.engstruct.2012.09.013

Cited by 42 publications

(26 citation statements)

References 40 publications

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“…A size-dependent behaviour was also noted experimentally for foams (Lakes 1983, Hütter 2016, concrete (Syroka-Korol et al 2013) and biological tissues (Choi et al 1990) and also numerically for random matrix-inclusion composites (Ostoja-Starzewski 1998), periodic composites (Pecullan et al 1999, Wang et al 2009) and unidirectional fibre reinforced composites (Jiang et al 2001). This behaviour may be described by the micropolar (or Cosserat) elasticity (Eringen 1999) as a dependence on the ratio of the dimension of the volume element to the characteristic length of its inner micro-structure (Wheel et al 2015).…”

Section: Introductionmentioning

confidence: 80%

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Daszkiewicz

Maquer

Zysset

2016

Biomech Model Mechanobiol

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word count: 249 Total word count: 3393Attachments: 5 figures and 2 tables + 1 figure and 4 tables in the appendices 2 Disclosure pageThe authors have no conflict of interest to report. AcknowledgmentsThe script manager Medtool (www.dr-pahr.at) was used to generate the µFE models, start the computations and analyse the results. The authors would like to thank Prof. Bert van Rietbergen for sharing the µCT data. Karol Daszkiewicz is supported by grants from the are also gratefully acknowledged. AbstractBoundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from µCT scans of femoral heads and vertebral bodies. They were converted into µFE models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs-and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors and model parameters ν0 (Poisson's ratio), E0 and µ0 (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on ν0. However, KUBCs-and PMUBCs-based E0 and µ0 respectively decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

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Section: Introductionmentioning

confidence: 80%

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Daszkiewicz

Maquer

Zysset

2016

Biomech Model Mechanobiol

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“…The ratio GF/Gf=1.42 was found by Bazant and Hoover [7] to fit all experimental results. Material parameters used in our study [Tab.1] were kept the same for all geometries and most of them where measured experimentally by Hoover et.al.…”

Section: Concrete Modelmentioning

confidence: 70%

“…In the calculations, the softening parameter in tension  was assumed to be non-local    [7]. As a weighting function, a Gauss distribution function was used.…”

Section: Concrete Modelmentioning

confidence: 99%

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FE analysis of a coupled energetic-statistical size effect in plain concrete beams with varying material properties

Korol¹,

Tejchman-Konarzewski²

2016

Proceedings of the 9th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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Abstract:The numerical FE investigations of a coupled energetic-statistical size effect in unnotched concrete beams of similar geometry under quasi-static three point bending were performed within elasto-plasticity with non-local softening. The stochastic FE analyses were carried out with three different beam sizes. Deterministic calculations were performed with the uniform distribution of a uniaxial tensile strength. In statistical calculations cross-correlated random fields were used to describe the spatial fluctuation of material randomness. Stochastic simulations were made with varying uniaxial tensile strength, initial fracture energy and elastic modulus. The effect of independently and simultaneously varying material parameter was investigated.

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“…All of the fracture models mentioned above are widely accepted by researchers and they are able to describe the size effect of concrete by including a characteristic length of concrete microstructure. In addition, the constitutive models with nonlocal softening [50][51][52][53][54][55][56][57] considering of the structural damage are also employed in the investigation of size effect in concrete structures and great progresses have been made. These kinds of fracture mechanical models predict a size effect if geometrically similar specimens (including notches) of different sizes are considered, such that the nominal strength r Nu decreases as the characteristic dimension D of the structure increases.…”

Section: Size Effect Analysis Based On Fracture Mechanicsmentioning

confidence: 99%

Mechanical behavior and size effect of moderate high-strength RC columns under monotonic and cyclic axial compression

Jin

Liu

2016

Engineering Structures

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FE calculations of a deterministic and statistical size effect in concrete under bending within stochastic elasto-plasticity and non-local softening

Cited by 42 publications

References 40 publications

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

FE analysis of a coupled energetic-statistical size effect in plain concrete beams with varying material properties

Mechanical behavior and size effect of moderate high-strength RC columns under monotonic and cyclic axial compression

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