A Probabilistic Crack Band Model for Quasibrittle Fracture

2016 ◽  
Vol 83 (5) ◽  
Author(s):  
Jia-Liang Le ◽  
Jan Eliáš
Keyword(s):  
Probability Distributions ◽  
Distribution Functions ◽  
Material Strength ◽  
Band Model ◽  
Quasibrittle Fracture ◽  
Damage Initiation ◽  
Nominal Strength ◽  
Crack Band ◽  
Random Location ◽  
Constitutive Parameters

This paper presents a new crack band model (CBM) for probabilistic analysis of quasibrittle fracture. The model is anchored by a probabilistic treatment of damage initiation, localization, and propagation. This model regularizes the energy dissipation of a single material element for the transition between damage initiation and localization. Meanwhile, the model also takes into account the probabilistic onset of damage localization inside the finite element (FE) for the case where the element size is larger than the crack band width. The random location of the localization band is related to the random material strength, whose statistics is described by a finite weakest link model. The present model is applied to simulate the probability distributions of the nominal strength of different quasibrittle structures. It is shown that for quasibrittle structures direct application of the conventional CBM for stochastic FE simulations would lead to mesh-sensitive results. To mitigate such mesh dependence, it is essential to incorporate the strain localization mechanism into the formulation of the sampling distribution functions of material constitutive parameters.

scholarly journals Verb valency in interlanguage: An extension to valency theory and new perspective on L2 learning

2020 ◽  
Vol 56 (2) ◽  
pp. 339-363
Author(s):  
Qianying Zhao ◽  
Jingyang Jiang
Keyword(s):  
Probability Distributions ◽  
Specific Property ◽  
Distribution Functions ◽  
Target Language ◽  
Native Languages ◽  
Language Competence ◽  
English Writing ◽  
Chinese Learners ◽  
L2 Learning ◽  
New Perspective

AbstractValency theory has been applied to investigate various languages, such as German, Chinese and English. However, most studies in this field were based on the linguistic materials produced by native speakers. The current research aimed to examine the valency structures in the interlanguage. Based on the English writing produced by L2 Chinese learners, we adopted the quantitative approach, trying to find out whether the distributional features of verb valency in the interlanguage also had regular probability distributions as those in the native languages, and whether there was a relationship between these valency distributional characteristics and L2 learners’ language competence. It was found that (1) verb valency in the interlanguage followed distributional regularities which had been identified in the native languages; (2) the valency features showed differences in the diversity of valency patterns, the use of valences and the complexity of forms of complements between the interlanguage and the target language; (3) the distribution functions and parameters related to verb valency could manifest the development of students’ language competence. The current research has extended valency theory to the study of interlanguage and the valency perspective has profound methodological and pedagogical implications for L2 learning. Its item-specific property and the integration of grammatical and lexical factors are conducive to analyzing the way various words combine with each other.

scholarly journals Probabilistic Precipitation Forecast Postprocessing Using Quantile Mapping and Rank-Weighted Best-Member Dressing

2018 ◽  
Vol 146 (12) ◽  
pp. 4079-4098 ◽  
Author(s):  
Thomas M. Hamill ◽  
Michael Scheuerer
Keyword(s):  
Probability Distributions ◽  
The United States ◽  
Ensemble Forecast ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Precipitation Forecast ◽  
Prediction System ◽  
Quantile Mapping ◽  
State Dependent ◽  
Grid Points

Abstract Hamill et al. described a multimodel ensemble precipitation postprocessing algorithm that is used operationally by the U.S. National Weather Service (NWS). This article describes further changes that produce improved, reliable, and skillful probabilistic quantitative precipitation forecasts (PQPFs) for single or multimodel prediction systems. For multimodel systems, final probabilities are produced through the linear combination of PQPFs from the constituent models. The new methodology is applied to each prediction system. Prior to adjustment of the forecasts, parametric cumulative distribution functions (CDFs) of model and analyzed climatologies are generated using the previous 60 days’ forecasts and analyses and supplemental locations. The CDFs, which can be stored with minimal disk space, are then used for quantile mapping to correct state-dependent bias for each member. In this stage, the ensemble is also enlarged using a stencil of forecast values from the 5 × 5 surrounding grid points. Different weights and dressing distributions are assigned to the sorted, quantile-mapped members, with generally larger weights for outlying members and broader dressing distributions for members with heavier precipitation. Probability distributions are generated from the weighted sum of the dressing distributions. The NWS Global Ensemble Forecast System (GEFS), the Canadian Meteorological Centre (CMC) global ensemble, and the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble forecast data are postprocessed for April–June 2016. Single prediction system postprocessed forecasts are generally reliable and skillful. Multimodel PQPFs are roughly as skillful as the ECMWF system alone. Postprocessed guidance was generally more skillful than guidance using the Gamma distribution approach of Scheuerer and Hamill, with coefficients generated from data pooled across the United States.

scholarly journals Size Effect in Fracture of Sandwich Structure Components: Foam and Laminate

2001 ◽  
Author(s):  
Zdeněk P. Bažant ◽  
Yong Zhou ◽  
Drahomír Novák ◽  
Isaac M. Daniel
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Sandwich Structure ◽  
Maximum Load ◽  
Material Strength ◽  
Large Structures ◽  
Nominal Strength ◽  
Sandwich Plates And Shells ◽  
Extensive Test ◽  
Plates And Shells

Abstract In the design of sandwich plates and shells for very large structures, such as ships in the range of 100 m length, it is very important to take the size effect on the nominal strength into account, and do so in a realistic, physically justified, manner. Before the size effect is addressed for a sandwich structure, it must be understood for its components — the foam core and the laminate skins. In the current practice, the size effects are automatically attributed to the randomness of material strength, as described by the Weibull theory. The purpose of this paper is to show that in both the foam and the laminate there are deterministic size effects, which are generally more pronounced. They are caused by stress redistribution and energy release due to the growth of large fractures or large cracking zones prior to attaining the maximum load. This deterministic size effect is verified and calibrated by new tests of notched specimens of rigid close-cell vinyl foam. A combined deterministic-probabilistic theory of size effect of the laminates is proposed and verified by extensive test data.

A Continuum Damage Model for Functionalized Graphene Membranes Based on Atomistic Simulations

2017 ◽  
Vol 754 ◽  
pp. 173-176
Author(s):  
Ivano Benedetti ◽  
R.A. Soler-Crespo ◽  
A. Pedivellano ◽  
Wei Gao ◽  
H.D. Espinosa
Keyword(s):  
Continuum Model ◽  
Damage Model ◽  
Atomistic Simulations ◽  
Band Model ◽  
Continuum Damage ◽  
Two Phase ◽  
Elastic Continuum ◽  
Continuum Damage Model ◽  
Crack Band ◽  
Hyper Elastic

A continuum model for GO membranes is developed in this study. The model is built representing the membrane as a two-dimensional, heterogeneous, two-phase continuum and the constitutive behavior of each phase (graphitic or oxidized) is built based on DFTB simulations of representative patches. A hyper-elastic continuum model is employed for the graphene areas, while a continuum damage model is more adequate for representing the behavior of oxidized regions. A finite element implementation for GO membranes subjected to degradation and failure is then implemented and, to avoid localization instabilities and spurious mesh sensitivity, a simple crack band model is adopted. The developed implementation is then used to investigate the existence of GO nano-representative volume elements.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

Microplane Model for Fracturing Damage of Triaxially Braided Fiber-Polymer Composites

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Ferhun C. Caner ◽  
Zdeněk P. Bažant ◽  
Christian G. Hoover ◽  
Anthony M. Waas ◽  
Khaled W. Shahwan
Keyword(s):  
Present Model ◽  
Material Model ◽  
Multiscale Model ◽  
Stress And Strain ◽  
Band Model ◽  
Braided Composites ◽  
Microplane Model ◽  
Explicit Finite Element ◽  
Crack Band ◽  
Strain Tensors

A material model for the fracturing behavior for braided composites is developed and implemented in a material subroutine for use in the commercial explicit finite element code ABAQUS. The subroutine is based on the microplane model in which the constitutive behavior is defined not in terms of stress and strain tensors and their invariants but in terms of stress and strain vectors in the material mesostructure called the “microplanes.” This is a semi-multiscale model, which captures the interactions between inelastic phenomena such as cracking, splitting, and frictional slipping occurring on planes of various orientations though not the interactions at a distance. To avoid spurious mesh sensitivity due to softening, the crack band model is adopted. Its band width, related to the material characteristic length, serves as the localization limiter. It is shown that the model can realistically predict the orthotropic elastic constants and the strength limits. More importantly, the present model can also fit the tests of size effect on the strength of notched specimens and the post-peak behavior, which have been conducted for this purpose. When used in the ABAQUS software, the model gives a realistic picture of the axial crushing of a braided tube by a divergent plug.

Probability distributions for the strength of fibrous materials under local load sharing I: Two-level failure and edge effects

1982 ◽  
Vol 14 (01) ◽  
pp. 68-94 ◽  
Author(s):  
D. Gary Harlow ◽  
S. Leigh Phoenix
Keyword(s):  
Edge Effects ◽  
Upper Bound ◽  
Fiber Strength ◽  
Probability Distributions ◽  
Probability Model ◽  
Load Sharing ◽  
Local Load ◽  
Material Strength ◽  
Fibrous Materials ◽  
Fiber Element

The focus of this paper is on obtaining a conservative but tight bound on the probability distribution for the strength of a fibrous material. The model is the chain-of-bundles probability model, and local load sharing is assumed for the fiber elements in each bundle. The bound is based upon the occurrence of two or more adjacent broken fiber elements in a bundle. This event is necessary but not sufficient for failure of the material. The bound is far superior to a simple weakest link bound based upon the failure of the weakest fiber element. For large materials, the upper bound is a Weibull distribution, which is consistent with experimental observations. The upper bound is always conservative, but its tightness depends upon the variability in fiber element strength and the volume of the material. In cases where the volume of material and the variability in fiber strength are both small, the bound is believed to be virtually the same as the true distribution function for material strength. Regarding edge effects on composite strength, only when the number of fibers is very small is a correction necessary to reflect the load-sharing irregularities at the edges of the bundle.

scholarly journals Development and Evaluation of Crack Band Model Implemented Progressive Failure Analysis Method for Notched Composite Laminate

2019 ◽  
Vol 9 (24) ◽  
pp. 5572
Author(s):  
Donghyun Yoon ◽  
Sangdeok Kim ◽  
Jaehoon Kim ◽  
Youngdae Doh
Keyword(s):  
Failure Analysis ◽  
Failure Criterion ◽  
Composite Laminate ◽  
Progressive Failure ◽  
Numerical Results ◽  
Band Model ◽  
Failure Initiation ◽  
Progressive Failure Analysis ◽  
Crack Band ◽  
Tension And Compression

Progressive failure analysis (PFA) is widely used to predict the failure behavior of composite materials. As a structure becomes more complex with discontinuities, prediction of failure becomes more difficult and mesh dependence must be taken into account. In this study, a PFA model was developed using the Hashin failure criterion and crack band model. The failure initiation was evaluated using the Hashin failure criterion. If failure initiation occurred, the damage variables at each failure mode (fiber tension and compression; matrix tension and compression) were calculated according to linear softening degradation and they were then used to derive the damaged stiffness matrix. This matrix reflected a degraded material, and PFA was continued until the damage variables became “1,” implying complete material failure. A series of processes were performed using the finite element method program ABAQUS with a user-defined material subroutine. To evaluate the proposed PFA model, experimental results of open-hole composite laminate tests were compared with the obtained numerical results. The strain behaviors were compared using a digital image correlation system. The obtained numerical results were in good agreement with the experimental ones.

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