On Stochastic Modeling of Interface Defects in Composite Materials

Kamiński, Marcin; Kleiber, Michał

doi:10.1080/107594100305429

Cited by 4 publications

(5 citation statements)

References 28 publications

(36 reference statements)

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“…In the computational experiments reported in Section 4.1 a linear decrease of the expected values E[C GHIJ ( )] and a nonlinear increase of the coe$cients of variation (C GHIJ ( )) have been observed with an increase of the total number of the interface defects considered. These tendencies are quite similar to those typical for probabilistically averaged elastic constants of an equivalent material in the interphase region [60]. At the same time the e!ect of the increase of the defects volume expected values depends on the e!ective tensor component implying an increase of E[C ( )], E[C ( )] and a decrease of E[C ( )].…”

Section: Discussionsupporting

confidence: 75%

“…Comparing the coe$cients of variation (C GHIJ ( )) collected in Figures 20}23 and Figures 24}27 a non-linear increase of these coe$cients with a DB increase can be observed in all tests. This dependence has a character similar to the behaviour of coe$cient of variation of the Young's modulus obtained during the interphase probabilistic averaging [60]. Moreover, all results are in the range of [0)00, 0)12] for all the numerical tests, being negligibly greater than the maximum value of (e ).…”

Section: Probabilistic Moments Of the Ewective Elasticity Tensorsupporting

confidence: 74%

“…Internal automatic generator for the square RVE with centrally located round "ber occupying about 50 per cent of the RVE with interface defects has been used (the in#uence of "ber radius variation on the stochastic displacements and stress "elds has been discussed previously in [58]. Considering greater composite sensitivity to the matrix defects (&bubbles'), which was proved numerically in [57,60], only composites having such discontinuities have been homogenized. The elastic constants for the "ber material have been taken as follows: E[e ]"84 GPa, "0)22 and the coe$cient of Young's modulus variation (e )"0)1, and for matrix E[e ]"4 GPa, "0)34.…”

Section: Probabilistic Moments Of the Ewective Elasticity Tensormentioning

confidence: 99%

“…Stochastic geometry was replaced by a deterministic one and the defects were probabilistically averaged [57,60] in the interphase region. In the present paper the random composite so de"ned with averaged elastic characteristic in the interphase will be homogenized using the e!ective modules method [5, 10}12] and the Monte-Carlo simulation technique [40,44].…”

mentioning

confidence: 99%

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Numerical homogenization ofN-component composites including stochastic interface defects

ski

Kleiber

2000

Int. J. Numer. Meth. Engng.

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The purpose of this paper is to present a mathematical formulation and numerical analysis for a homogenization problem of random elastic composites with stochastic interface defects. The homogenization of composites so de"ned is carried out in two steps: (i) probabilistic averaging of stochastic discontinuities in the interphase region, (ii) probabilistic homogenization by extending the e!ective modules method to media random in the micro-scale. To obtain such an approach the classical mathematical homogenization method is formulated for n-component composite with random elastic components and implemented in the FEMbased computer program. The article contains also numerous computational experiments illustrating stochastic sensitivity of the model to interface defects parameters and verifying statistical convergence of probabilistic simulation procedure. saturated media [20}22]. Nowadays, in deterministic homogenization, new numerical methods have been developed such as the self-consistent Mori}Tanaka model [23] or FEM-like bounds on e!ective properties [24]; numerous new applications of known methods have been discussed [25,26]. On the other hand, problems of composites strength in the context of their e!ective properties [27,28], homogenization of multiphase media [29], inverse homogenization problems [30] and many others have also been studied. It should be underlined that the problem discussed is very often related to optimization techniques [28,31,32] being an important aspect considering numerous engineering applications of the latter. Such problems are solved by using variational upper and lower bounds of the e!ective composite characteristics [28,33,34].Stochastic concepts in the area of homogenization appeared "rst in the late 1960s [1]. They gradually evolved in the 1970s [35] and 1980s [36}38], but these approaches were either simple variational upper and lower bounds or did not lead to any numerical realizations. Advanced mathematical theories [39, 40] and computational methodologies have been emerging only recently. The most important appears to be: the Delaunay networks approach [41], the Voronoi Cell Finite Element Method [42}43] and the Monte-Carlo method [40, 44].All the methods developed so far, no matter whether deterministic or probabilistic, have one general disadvantage*they as a rule neglect defects appearing on the boundary between the composite components (some deterministic models were presented in [5, 45}46]). It has been proved by laboratory tests that these defects are the dominating factors in the evaluation of non-linear behavior and the strength of composite structures [47,48]. There are many recent papers dealing with deterministically modeled interface defects considering physical mechanisms [47,49] and computational aspects [50}52]. On the other hand, the micro-mechanical formulations for the contact problems [53}56] neglect their real random character e!ectively considering the expected values of these defects only.A "rst formulation for a random composite with stochastic interf...

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Section: Discussionsupporting

confidence: 75%

Section: Probabilistic Moments Of the Ewective Elasticity Tensorsupporting

confidence: 74%

Section: Probabilistic Moments Of the Ewective Elasticity Tensormentioning

confidence: 99%

mentioning

confidence: 99%

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Numerical homogenization ofN-component composites including stochastic interface defects

ski

Kleiber

2000

Int. J. Numer. Meth. Engng.

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“…This result is very robust, and the details of the fit can be found elsewhere 31,33 . In related data, a drop in the quasiparticle scattering rate below this energy scale is observed 31,32 , which is consistent with optics data reporting a rapid drop of the scattering rate, 1/τ , at similar energy 35 . The observed behavior, a sudden change in the dispersion and a drop in the scattering rate, is very reminiscent of quasiparticle coupled to a sharp collective mode.…”

supporting

confidence: 78%

Role of the electron-phonon interaction in the strongly correlated cuprate superconductors

Shen

Lanzara

Ishihara

et al. 2002

Philosophical Magazine B

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Using high resolution angle-resolved photoemission data in conjunction with that from neutron and other probes, we show that electron-phonon (el-ph) coupling is strong in cuprates superconductors and it plays an important role in pairing. In addition to the strong electron correlation, the inclusion of phonons provides a theoretical framework explaining many important phenomena that cannot be understood by a strongly correlated electronic model alone. Especially it is indispensable to explain the difference among materials. The phonons with the wave number around the (0, qx) and (qx, 0) axes create the d-wave pairing while that near (π, π) are pair breaking. Therefore the half-breathing mode of the oxygen motions helps d-wave superconductivity.PACS numbers: 79.60. Bm, 73.20.Dx, It has been a long-standing question whether a strongly correlated electronic model of the CuO 2 plane, such as the t-J or Hubbard model alone, can explain the essential experimental observation of superconductivity in cuprates oxides. On the one hand, such a model has been remarkably successful in explaining many important physical properties, most notably the property of the undoped insulator and the renormalization of charge dynamics in it, by spin dynamics from t to J scale 1,2 and in predicting a spin gap 3-5 . On the other hand, important questions have been raised. The first is the observation that, while the CuO 2 plane conductivity is essentially the same for various families of cuprates, their T c vary by at least an order of magnitude 6,7 . The second is the observation that the phonons and lattice effects are clearly present in these materials 8 , following the original assumption that the Jahn-Teller (JT) polarons might be important for superconductivity 9 . There is currently no consensus on the above issues.Within the context of cuprates superconductors, it is difficult to understand some of the material specific properties by considering only the electronic degree of freedom. Fig. 1a summarizes the systematic in the superconducting gap size (∆), together with the transition temperature (T c ) shown in Fig. 1c. Unlike T c , which can be depressed by phase fluctuations in the underdoped regime 10-12 , the superconducting gap essentially reflects the pairing strength. It can be clearly seen that the pairing strength for the p-type cuprates is very strong, with gap sizes that are at least an order of magnitude larger than conventional superconductors. Further, the maximum T c of each family is controlled by the maximum superconducting gap size. This is most dramatically illustrated by the HgBa 2 Ca n−1 Cu n O 2(n+1) (Hg1223 for n=3) compound, which has a much larger gap size as well as T c . Fig 1a also clearly shows a discrepancy between pand n-type materials, as superconductivity in a n-type material appears to be very fragile with a much weaker pairing strength. The electron-hole asymmetry is particularly perplexing in the context of spin pairing only, as magnetism is very strong and persists to a much wider range in the n-...

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Machine learning based probabilistic model for free vibration analysis of functionally graded graphene nanoplatelets reinforced porous plates

Shakir

Talha

Dileep

2023

Mechanics of Advanced Materials and Structures

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On Stochastic Modeling of Interface Defects in Composite Materials

Cited by 4 publications

References 28 publications

Numerical homogenization ofN-component composites including stochastic interface defects

Numerical homogenization ofN-component composites including stochastic interface defects

Role of the electron-phonon interaction in the strongly correlated cuprate superconductors

Machine learning based probabilistic model for free vibration analysis of functionally graded graphene nanoplatelets reinforced porous plates

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