A probabilistic model for spatial distribution of material properties

Shinozuka, Masanobu; Lenoe, E. M.

doi:10.1016/0013-7944(76)90087-4

Cited by 65 publications

(13 citation statements)

References 4 publications

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“…All these methods have been summarized in [7,14,24]. The probabilistic methods have found numerous applications in modeling of material properties randomness of solids [19,37] as well as fracture processes in composites [17,40,42].…”

mentioning

confidence: 99%

On Stochastic Modeling of Interface Defects in Composite Materials

Kamiński¹,

Kleiber²

2000

Mech. of Adv. Mat. & Structures

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The article presents mathematical and computational research dealing with the problem of stochastic interface defects occurring in composite materials between their constituents. A mathematical model of the periodic composite with such defects is presented in detail, as well as probabilistic numerical methods enabling computational experiments which are shown in a further part of the text. The ber-reinforced and laminated composite has been tested in numerical tests as well as the superconducting coil cable-four-component composite to verify how the structural defects considered, according to the model introduced, in uence the static behavior of the composites analyzed. All the results obtained and discussed in the article are summarized in concluding remarks which show the directions of further model development, while numerous references enable the reader to study the problem further.The rst mathematical theories dealing with composite materials assumed that their mechanical properties depend on elastic characteristics of the constituents [13]. It was an effect of the mathematical model that components of the composite were assumed to be perfectly bonded. However, experimental practice in composite engineering shows that the overall behavior of multicomponent structures is determined mainly by the quality of the component materials bonding [27]. The structural defects occurring on the composite interfaces are caused by the technological problems resulting generally from thermal incompatibility of composite constituents and interfacial stress concentrations. On the other hand, the quality of composite constituents bonds is worsened by the different kinds of degradation processes caused by the water penetration of composite interfaces. The presence of water on the interfaces can cause swelling and plasti cation of the matrix and of the capillary tubes along the interface boundaries in the direction parallel to the ber orientation. The phenomena described above may lead to interphase debonding, interfacial sliding [22,33], and even to ber pull-out, and they have been described in detail in [20,32].All the interface phenomena have been worked out through numerous nite-element implementations based generally on the special interface-type nite elements [21,34,35],

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confidence: 99%

On Stochastic Modeling of Interface Defects in Composite Materials

Kamiński¹,

Kleiber²

2000

Mech. of Adv. Mat. & Structures

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“…B. [2], [3], [4], [4a]) existieren analytische Methoden, die sich auf die klassische Wahrscheinlichkeitsrechnung berufen. Das Interesse gilt den statistischen Momenten oder den Verteilungsfunktionen der sicherheitsrelevanten Zustandsgrößen.…”

Section: Einführungunclassified

Zur probabilistischen Sicherheitsanalyse von Stabtragwerken nach der Theorie 2. Ordnung

Biehounek

Grolik

2008

Stahlbau

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Das probabilistische Bemessungsverfahren für Stabtragwerke geht aus der Deformationsmethode nach der Theorie 2. Ordnung hervor und bewahrt die auf dem Gleichgewicht der Kräfte und Drehmomente beruhende Praxis. Die Approximation zufälliger Lasten durch Hermitesche Polynome normalverteilter Zufallsgrößen führt mittels Galerkin‐Projektion auf ein lineares Gleichungssystem. Es beruht auf der Elastizitätsgleichung der deterministischen Deformationsmethode und muss iterativ behandelt werden. Das Verfahren lässt sich formalisieren und liefert die Versagenswahrscheinlichkeit mit einem im Berufsalltag des Bauingenieurs vertretbaren Aufwand. An Hand des Querschnittsversagens wird gezeigt, in welcher Hinsicht die probabilistische Analyse das mit Beiwerten arbeitende Sicherheitskonzept erweitert.

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“…[23][24][25][26][27] However, almost all the conventional FEA methods set uniform fracture parameters for each part of the materials. Some reports also considered the effects of the stochastic variability in fracture properties, [28][29][30] stochastic variability of the geometric shape of the microscopic structure by multiscale analysis of CMC, 22 and the slit-type defect distribution on a mesoscale model, which approximately imitates the micro-crack and/or grain boundary type of flaw. 31 However, to the best of the author's knowledge, previous FEA methods have not yet predicted the scatter in bulk stiffness and strength induced by the pore and grain size distribution.…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis of fracture statistics of ceramics: Effects of grain size and pore size distributions

et al. 2018

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A novel numerical simulation method based on finite element analysis (FEA), which can evaluate the fracture probability caused by the characteristics of flaw distribution, is considered an effective tool to facilitate and increase the use of ceramics in components and members. In this study, we propose an FEA methodology to predict the scatter of ceramic strength. Specifically, the data on the microstructure distribution (i.e., relative density, size and aspect ratio of pore, and grain size) are taken as the input values and reflected onto the parameters of a continuum damage model via a fracture mechanical model based on the circumferential circular crack emanating from an oval spherical pore. In addition, we numerically create a Weibull distribution based on multiple FEA results of a three‐point bending test. Its validity is confirmed by a quantitative comparison with the actual test results. The results suggest that the proposed FEA methodology can be applied to the analysis of the fracture probability of ceramics.

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A probabilistic model for spatial distribution of material properties

Cited by 65 publications

References 4 publications

On Stochastic Modeling of Interface Defects in Composite Materials

On Stochastic Modeling of Interface Defects in Composite Materials

Zur probabilistischen Sicherheitsanalyse von Stabtragwerken nach der Theorie 2. Ordnung

Finite element analysis of fracture statistics of ceramics: Effects of grain size and pore size distributions

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