Phenomena of Multicale Fracture of Brittle Materials and its Application to Teaching in Strength Theory

2011 ◽  
Vol 243-249 ◽  
pp. 2084-2090 ◽  
Author(s):  
Li Wang ◽  
Da Hu Rui ◽  
Jian Hui Yang
Keyword(s):  
Brittle Material ◽  
Tensile Strain ◽  
Failure Process ◽  
Strength Theory ◽  
Multi Scale ◽  
Scale Size ◽  
Micro Cracks ◽  
Macro Scale ◽  
Shearing Strain ◽  
Meso Scale

Multi-scale science is the challenge and opportunity of science in the 21th century, and turbulence of liquid and fracture of solid will be the classical problems of multi-scale mechanics. The failure process of brittle materials displayed a multi-scale mechanics feature that amounts of micro damages grow large trans-scale and nonlinear and evolve to a macro catastrophic transition in the end. So, the concepts of scale and hierarchy of material are inescapable in strength theory to be used explaining solid fracture, it is the main puzzle of the strength theory at present. In the paper, in order to show the phenomena of multi-scale fracture, numeric method is used to simulate the failure process of brittle material, during which micro cracks initiate, grow large, aggregate and in the end form a run-through fracture band in the sample. The result of the numeric simulation shows that the micro cracks of a meso-scale size initiate due to tensile strain and the sample of a macro-scale size breaks down due to tensile-shearing strain under uniaxial tensile or due to compression-shearing strain under uniaxial compression. It powerfully disabused the puzzles in teaching strength theory of brittle material. The further discussion concluded that for a brittle material grain of meso-scale size, the theory of Maximum Tensile Strain is reasonable in explaining the strength, as for a brittle material sample of a macro-scale size, the mohr-columb theory is reasonable for its strength owing to the two important factors of cohesive strength and friction factorwere introduced.

Application of an EMMS Model for Bubbly Fluidized Bed

2017 ◽  
Vol 372 ◽  
pp. 170-179
Author(s):  
Daniel A. Kestering ◽  
Flavia F.S. Zinani ◽  
George C. Bleyer
Keyword(s):  
Multi Scale ◽  
Macro Scale ◽  
Scale Models ◽  
Fluid Bed ◽  
Computational Fluid Dynamics Cfd ◽  
Geldart Groups ◽  
Coarse Grids ◽  
Individual Particles ◽  
Meso Scale ◽  
Good Agreement

In computational fluid dynamics (CFD) of fluidization processes, the modeling of drag between fluid and particles has a direct effect on the results. The EMMS (Energy Minimization Multi-Scale) models are based on the micro-scale of individual particles and the macro scale of equipment to model the meso-scale phenomena related to particle clustering, which directly affect the drag between fluid and particles. The EMMS/bubbling model was introduced as a change from the classic EMMS model to specific bubbling fluid bed conditions. The present work aims to apply the EMMS/bubbling model in the CFD of Geldart-D particles fluidized by air. The results were compared with results from the literature. It was observed that, for particles of Geldart groups A and B, the results using the EMMS/bubbling model agreed well with the literature. The CFD results for Geldart-D particles showed good agreement with the literature results for this method using coarse grids.

scholarly journals Bayesian stochastic multi-scale analysis via energy considerations

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Muhammad S. Sarfaraz ◽  
Bojana V. Rosić ◽  
Hermann G. Matthies ◽  
Adnan Ibrahimbegović
Keyword(s):  
Nonlinear Approximation ◽  
Computational Cost ◽  
Cementitious Materials ◽  
Model Errors ◽  
Stored Energy ◽  
Standard Material ◽  
Multi Scale ◽  
Macro Scale ◽  
Optimal Material ◽  
Meso Scale

AbstractMulti-scale processes governed on each scale by separate principles for evolution or equilibrium are coupled by matching the stored energy and dissipation in line with the Hill-Mandel principle. We are interested in cementitious materials, and consider here the macro- and meso-scale behaviour of such a material. The accurate representations of stored energy and dissipation are essential for the depiction of irreversible material behaviour, and here a Bayesian approach is used to match these quantities on different scales. This is a probabilistic upscaling and as such allows to capture, among other things, the loss of resolution due to scale coarsening, possible model errors, localisation effects, and the geometric and material randomness of the meso-scale constituents in the upscaling. On the coarser (macro) scale, optimal material parameters are estimated probabilistically for certain possible behaviours from the class of generalised standard material models by employing a nonlinear approximation of Bayes’s rule. To reduce the overall computational cost, a model reduction of the meso-scale simulation is achieved by combining unsupervised learning techniques based on a Bayesian copula variational inference with functional approximation forms.

Experiment-based validation and uncertainty quantification of coupled multi-scale plasticity models

2016 ◽  
Vol 12 (1) ◽  
pp. 151-176 ◽  
Author(s):  
Garrison Stevens ◽  
Sez Atamturktur ◽  
Ricardo Lebensohn ◽  
George Kaschner
Keyword(s):  
Coupled Model ◽  
Material Behavior ◽  
Radioactive Material ◽  
Material Structure ◽  
Coupled Models ◽  
Content Type ◽  
Strongly Coupled ◽  
Multi Scale ◽  
Macro Scale ◽  
Meso Scale

Purpose – Highly anisotropic zirconium is a material used in the cladding of nuclear fuel rods, ensuring containment of the radioactive material within. The complex material structure of anisotropic zirconium requires model developers to replicate not only the macro-scale stresses but also the meso-scale material behavior as the crystal structure evolves; leading to strongly coupled multi-scale plasticity models. Such strongly coupled models can be achieved through partitioned analysis techniques, which couple independently developed constituent models through an iterative exchange of inputs and outputs. Throughout this iterative process, biases, and uncertainties inherent within constituent model predictions are inevitably transferred between constituents either compensating for each other or accumulating during iterations. The paper aims to discuss these issues. Design/methodology/approach – A finite element model at the macro-scale is coupled in an iterative manner with a meso-scale viscoplastic self-consistent model, where the former supplies the stress input and latter represents the changing material properties. The authors present a systematic framework for experiment-based validation taking advantage of both separate-effect experiments conducted within each constituent’s domain to calibrate the constituents in their respective scales and integral-effect experiments executed within the coupled domain to test the validity of the coupled system. Findings – This framework developed is shown to improve predictive capability of a multi-scale plasticity model of highly anisotropic zirconium. Originality/value – For multi-scale models to be implemented to support high-consequence decisions, such as the containment of radioactive material, this transfer of biases and uncertainties must be evaluated to ensure accuracy of the predictions of the coupled model. This framework takes advantage of the transparency of partitioned analysis to reduce the accumulation of errors and uncertainties.

scholarly journals Effects of multi-scale heterogeneity on the simulated evolution of ice-rich permafrost lowlands under a warming climate

2021 ◽  
Vol 15 (3) ◽  
pp. 1399-1422
Author(s):  
Jan Nitzbon ◽  
Moritz Langer ◽  
Léo C. P. Martin ◽  
Sebastian Westermann ◽  
Thomas Schneider von Deimling ◽  
...  
Keyword(s):  
Climate Warming ◽  
Land Surface ◽  
Landscape Dynamics ◽  
Permafrost Degradation ◽  
Subgrid Scale ◽  
Feedback Mechanisms ◽  
Multi Scale ◽  
Macro Scale ◽  
Ice Wedge ◽  
Meso Scale

Abstract. In continuous permafrost lowlands, thawing of ice-rich deposits and melting of massive ground ice lead to abrupt landscape changes called thermokarst, which have widespread consequences on the thermal, hydrological, and biogeochemical state of the subsurface. However, macro-scale land surface models (LSMs) do not resolve such localized subgrid-scale processes and could hence miss key feedback mechanisms and complexities which affect permafrost degradation and the potential liberation of soil organic carbon in high latitudes. Here, we extend the CryoGrid 3 permafrost model with a multi-scale tiling scheme which represents the spatial heterogeneities of surface and subsurface conditions in ice-rich permafrost lowlands. We conducted numerical simulations using stylized model setups to assess how different representations of micro- and meso-scale heterogeneities affect landscape evolution pathways and the amount of permafrost degradation in response to climate warming. At the micro-scale, the terrain was assumed to be either homogeneous or composed of ice-wedge polygons, and at the meso-scale it was assumed to be either homogeneous or resembling a low-gradient slope. We found that by using different model setups and parameter sets, a multitude of landscape evolution pathways could be simulated which correspond well to observed thermokarst landscape dynamics across the Arctic. These pathways include the formation, growth, and gradual drainage of thaw lakes; the transition from low-centred to high-centred ice-wedge polygons; and the formation of landscape-wide drainage systems due to melting of ice wedges. Moreover, we identified several feedback mechanisms due to lateral transport processes which either stabilize or destabilize the thermokarst terrain. The amount of permafrost degradation in response to climate warming was found to depend primarily on the prevailing hydrological conditions, which in turn are crucially affected by whether or not micro- and/or meso-scale heterogeneities were considered in the model setup. Our results suggest that the multi-scale tiling scheme allows for simulating ice-rich permafrost landscape dynamics in a more realistic way than simplistic one-dimensional models and thus facilitates more robust assessments of permafrost degradation pathways in response to climate warming. Our modelling work improves the understanding of how micro- and meso-scale processes affect the evolution of ice-rich permafrost landscapes, and it informs macro-scale modellers focusing on high-latitude land surface processes about the necessities and possibilities for the inclusion of subgrid-scale processes such as thermokarst within their models.

scholarly journals TBRs, a methodology for the multi-scalar cartographic analysis of the distribution of plant formations

2020 ◽  
Author(s):  
Rafael Cámara Artigas ◽  
Fernando Díaz del Olmo ◽  
Jose Ramon Martinez Batlle
Keyword(s):  
Water Balance ◽  
Distribution Map ◽  
Biomass Distribution ◽  
Micro Scale ◽  
Multi Scale ◽  
Macro Scale ◽  
Bioclimatic Variables ◽  
Different Levels ◽  
Meso Scale ◽  
Scale Classification

An analytical and cartographic method of biomass distribution and plant formations at a multi-scalar level is developed based on bioclimatic variables extracted from the Thornthwaite Water Balance (WB) and the Bioclimatic Balances (BB) of Montero de Burgos & González Rebollar. As a result, a distribution map involving Types of Bioclimatic Regimens (TBR) is obtained leading to the identification of a multi-scale classification at different levels: zonal (macro-scale) with 5 types, regional (meso-scale) with 27 types, and local (micro-scale) with 162 plant formations subtypes, conditioned by lithology-soils, the relief exposure to wind or sunstroke respectively and obtained through the combination of TBR and ombroclimates.

scholarly journals A Multi-Scale Modeling Approach for Simulating Crack Sensing in Polymer Fibrous Composites Using Electrically Conductive Carbon Nanotube Networks. Part II: Meso- and Macro-Scale Analyses

Aerospace ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 106 ◽  
Author(s):  
Konstantinos Tserpes ◽  
Christos Kora
Keyword(s):  
Carbon Nanotube ◽  
Fibrous Composites ◽  
Electrically Conductive ◽  
Micro Scale ◽  
Multi Scale ◽  
Modeling Approach ◽  
Scale Modeling ◽  
Macro Scale ◽  
Multi Scale Modeling ◽  
Meso Scale

This is the second of a two-paper series describing a multi-scale modeling approach developed to simulate crack sensing in polymer fibrous composites by exploiting interruption of electrically conductive carbon nanotube (CNT) networks. The approach is based on the finite element (FE) method. Numerical models at three different scales, namely the micro-scale, the meso-scale and the macro-scale, have been developed using the ANSYS APDL environment. In the present paper, the meso- and macro-scale analyses are described. In the meso-scale, a two-dimensional model of the CNT/polymer matrix reinforced by carbon fibers is used to develop a crack sensing methodology from a parametric study which relates the crack position and length with the reduction of current flow. In the meso-model, the effective electrical conductivity of the CNT/polymer computed from the micro-scale is used as input. In the macro-scale, the final implementation of the crack sensing methodology is performed on a CNT/polymer/carbon fiber composite volume using as input the electrical response of the cracked CNT/polymer derived at the micro-scale and the crack sensing methodology. Analyses have been performed for cracks of two different lengths. In both cases, the numerical model predicts with good accuracy both the length and position of the crack. These results highlight the prospect of conductive CNT networks to be used as a localized structural health monitoring technique.

scholarly journals A Multi-Scale Modeling Approach for Simulating Crack Sensing in Polymer Fibrous Composites Using Electrically Conductive Carbon Nanotube Networks. Part II: Meso- and Macro-Scale Analyses

2018 ◽  
Author(s):  
Konstantinos Tserpes ◽  
Christos Kora
Keyword(s):  
Carbon Nanotube ◽  
Fibrous Composites ◽  
Electrically Conductive ◽  
Micro Scale ◽  
Multi Scale ◽  
Modeling Approach ◽  
Scale Modeling ◽  
Macro Scale ◽  
Multi Scale Modeling ◽  
Meso Scale

This is the second of a two-paper series describing a multi-scale modeling approach developed to simulate crack sensing in polymer fibrous composites by exploiting interruption of electrically conductive carbon nanotube (CNT) networks. The approach is based on the finite element (FE) method. FE models at three different scales, namely the micro-scale, the meso-scale and the macro-scale, have been developed using the ANSYS PDL environment. In the present paper, the meso- and macro-scale analyses are described. In the meso-scale, a two-dimensional model of the CNT/polymer matrix reinforced by carbon fibers is used to develop a crack sensing methodology from a parametric study which relates the crack position and length with the reduction of current flow. In the meso-model, the effective electrical conductivity of the CNT/polymer computed from the micro-scale is used as input. In the macro-scale, the final implementation of the crack sensing methodology is performed on a CNT/polymer/carbon fiber composite volume using as input the electrical response of the cracked CNT/polymer derived at the micro-scale and the crack sensing methodology. Analyses have been performed for cracks of two different lengths. In both cases, the numerical model predicts with good accuracy both the length and position of the crack. These results highlight the prospect of conductive CNT networks to be used as a localized structural health monitoring technique.

Multi-Scale Investigation on Residual Strength of Jacket Platform With Fatigue Crack Damage

2015 ◽  
Author(s):  
Ren Hua Wang ◽  
Xiang Zou ◽  
Pei Lin Dou ◽  
Yuan Yuan Fang ◽  
Guang-en Luo
Keyword(s):  
Fatigue Crack ◽  
Residual Strength ◽  
Scale Structure ◽  
Scale Model ◽  
Wave Load ◽  
Jacket Platform ◽  
Multi Scale ◽  
Extreme Load ◽  
Macro Scale ◽  
Meso Scale

Fatigue crack damage caused by the wave load brings the structure of jacket platform in service potential failure risk when subjected to the extreme load. However, there is lack of efficient method to evaluate the influence of crack damage on the structural performance because of the huge scale difference between the meso-scale damage and the macro-scale structure. Based on the multi-scale finite element method (FEM), to improve the efficiency of structural analysis, the damaged region of the structure is modeled with fine FE mesh (shell element) to describe the fatigue crack, and the undamaged area is modeled with coarse FE mesh (beam element). Furthermore, the applicability and superiority of this multi-scale model was validated through comparing the results obtained from the beam, multi-scale and shell models. The influence of the time-varying crack damage on the residual strength of jacket platform is then revealed based on the multi-scale FE model. The results show that the proposed multi-scale method can accurately describe fatigue crack damage in the macro-scale structure, and be applied to investigate the influence of meso-scale structural damage under the extreme load condition.

Meso-Scale Experimental & Numerical Studies for Predicting Macro-scale Performance of Advanced Reactive Materials (ARMs)

2015 ◽  
Author(s):  
Naresh Thadhani ◽  
Arun Gokhale ◽  
Jason Quenneville ◽  
Jennifer Breidenich ◽  
Manny Gonzales ◽  
...  
Keyword(s):  
Reactive Materials ◽  
Numerical Studies ◽  
Macro Scale ◽  
Meso Scale

A novel synergistic multi-scale modeling framework to predict micro- and meso-scale damage behaviors of 2D triaxially braided composite

2021 ◽  
pp. 105678952110339
Author(s):  
Hongyong Jiang ◽  
Yiru Ren ◽  
Qiduo Jin
Keyword(s):  
Compressive Load ◽  
Scale Model ◽  
Modeling Framework ◽  
Braided Composite ◽  
Multi Scale ◽  
Scale Modeling ◽  
Bridge Model ◽  
Multi Scale Modeling ◽  
Transverse Damage ◽  
Meso Scale

A novel synergistic multi-scale modeling framework with a coupling of micro- and meso-scale is proposed to predict damage behaviors of 2D-triaxially braided composite (2DTBC). Based on the Bridge model, the internal stress and micro damage of constituent materials are respectively coupled with the stress and damage of tow. The initial effective elastic properties of tow (IEEP) used as the predefined data are estimated by micro-mechanics models. Due to in-situ effects, stress concentration factor (SCF) is considered in the micro matrix, exhibiting progressive damage accumulation. Comparisons of IEEP and strengths between the Bridge and Chamis’ theory are conducted to validate the values of IEEP and SCF. Based on the representative volume element (RVE), the macro properties and damage modes of 2DTBC are predicted to be consistent with available experiments and meso-scale simulation. Both axial and transverse damage mechanisms of 2DTBC under tensile or compressive load are revealed. Micro fiber and matrix damage accumulations have significant effects on the meso-scale axial and transverse damage of tows due to multi-scale coupling effects. Different from existing meso-/multi-scale models, the proposed multi-scale model can capture a crucial phenomenon that the transverse damage of tow is vulnerable to micro fiber fracture. The proposed multi-scale framework provides a robust tool for future systematic studies on constituent materials level to larger-scale aeronautical materials.

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