Stochastic modeling of multi-filament yarns: II. Random properties over the length and size effect

Vořechovský, Miroslav; Chudoba, Rostislav

doi:10.1016/j.ijsolstr.2005.06.062

Cited by 62 publications

(48 citation statements)

References 20 publications

(29 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It studies the dependence of bar strength on l ρ with several different averaging lengths, l char . When l char → 0, the problem reduces to the problem of extremes of Weibullian random fields studied previously in [24,25]. When l char → ∞, the samples of random fields are random constant functions and the averaging does not modify the samples.…”

Section: Extremes Of Moving Averages Of 1d Random Fieldsmentioning

confidence: 98%

Interplay of probabilistic and deterministic internal length in simulations of concrete fracture

Eliáš¹,

Kaděrová²,

Vořechovský³

2016

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

View full text Add to dashboard Cite

Abstract. The contribution presents simulations of fracture in concrete beams loaded in three-point bending via discrete model. The size and distribution of discrete units reflect the concrete heterogeneity and together with properties of their contacts provide an internal length scale. Due to a random placement of the discrete units, the model mimics natural randomness of material structure arising from its random heterogeneity. A second random component of the model considered is additional fluctuation of material parameters at contacts between the units. This randomness reflects variations in material properties due to mixing, drying, etc. and it is considered in a form of random field with its own internal length scale provided in a form of autocorrelation length.By changing the ratios between the autocorrelation length and the internal length arising from heterogeneities, one can observe strong effects of this ratio on structural strength when cracks propagate from smooth surface. For deeply notched beams, the spatial strength fluctuations only affects the variance of the peak load and no significant effect observed on its mean value. The described dependency of structural strength on the ratio between the two characteristic lengths is demonstrated and elucidated.

show abstract

Section: Extremes Of Moving Averages Of 1d Random Fieldsmentioning

confidence: 98%

Interplay of probabilistic and deterministic internal length in simulations of concrete fracture

Eliáš¹,

Kaděrová²,

Vořechovský³

2016

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

View full text Add to dashboard Cite

show abstract

“…Here it should be noted that in most cases the spatial heterogeneity at arbitrary scale (meso, micro and macro) is irrelevant for the assessment of engineering structures made from basic construction materials, such as concrete, steel or wood. However, it becomes highly relevant to currently designed composites [11], structural details such as those of anchoring technology [12] or geotechnical assessment [13]. Similarly, the implicit treatment of spatial variability is important to the reliability based code calibration [14,15], design of experiments [16] and verification of various hypotheses or limit theorems, such as fracture behaviour or size effect [17].…”

Section: Small Sample Simulations For Spatial Variabilitymentioning

confidence: 99%

Implications of spatial variability characterization in discrete particle models

Podroužek¹,

Vorel²,

Boumakis³

et al. 2016

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

View full text Add to dashboard Cite

Characterization of the inherent spatial variability of the mechanical properties of advanced composite materials as well as of standard concretes is among the primary concerns of the presented paper. In the context of discrete particle models the random field concept is frequently adopted in order to account for the fluctuations of material characteristics on scales independent of the geometrical characterization of the mesostructure as represented by particular particle configurations mimicking the aggregate placement. The specific goal of this paper is to introduce spatial variability into structural reliability by providing a sample reduction strategy for the discrete framework. Presented simulations of a classical experiment utilize the well-established Lattice Discrete Particle Model (LDPM) and demonstrate the general potential of the proposed strategy towards current state-of-the-art in stochastic mechanics and some relating open problems.

show abstract

“…The breaking strain ξ is considered to be a random variable described by its probability density function (PDF) f ξ (e) (and CDF denoted as F ξ (e)). By definition of the mean value we can write that the average response of a fiber represents the mean response of a bundle with n → ∞ [8]:…”

Section: Improved Approximation Of the Standard Deviationmentioning

confidence: 99%

Improved Gaussian Approximation of the Bundle Strength of Daniels’ Model With Brittle Weibull Fibers

Sadílek¹,

Vořechovský²

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

View full text Add to dashboard Cite

Keywords: Fiber bundle model, strength of the bundle, Daniels bundle model, equal load sharing, Weibull distribution, cumulative distribution function.Abstract. The paper deals with the classical fiber bundle model with equal load sharing, sometimes referred to as the the Daniels bundle model or the democratic bundle. This model is significant for the strength of quasi-brittle structures and the reliability of many parallel systems.In the present paper, the authors exploit their own implementation of the recursive formula for the evaluation of the distribution function for fiber bundle strength. The implementation was carried out in the Python high-level programming language using the NumPy (scientific computing with arrays) and mpmath (library for real and complex floating-point arithmetic with arbitrary precision) packages. This implementation enables the calculation of cumulative distribution function values for large numbers (thousands) of fibers in a bundle, including values deep in the left tail of the distribution (probabilities 10 −600 ). This computer program has been used to accurately calculate the distribution functions for bundles with Weibull fibers with the unit scale parameter, the varying number of filaments and the varying shape parameter. A database of these distribution functions has been used to calculate the mean values and standard deviations of the peak force to propose an improved Gaussian approximation of bundle strength. 986

show abstract

Stochastic modeling of multi-filament yarns: II. Random properties over the length and size effect

Cited by 62 publications

References 20 publications

Interplay of probabilistic and deterministic internal length in simulations of concrete fracture

Interplay of probabilistic and deterministic internal length in simulations of concrete fracture

Implications of spatial variability characterization in discrete particle models

Improved Gaussian Approximation of the Bundle Strength of Daniels’ Model With Brittle Weibull Fibers

Contact Info

Product

Resources

About