Two‐Scale Simulation of a Disc With a Crack by X‐FEM and Cell Model
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Abstract The two‐scale simulation of a linear‐elastic orthotropic disc with a central crack under mode‐I loading may be used to verify the extended finite element method implementation of orthotropic enrichment functions into finite element codes such as FEAP. The stress distribution on the finer scale is simultaneously resolved by the high fidelity generalized method of cells called at each integration point of the macro elements. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)Keywords:
Orthotropic material
Macro
High fidelity
Mode (computer interface)
Macroscopic scale
Central to the quest for a deeper understanding of the cancer growth and spread process, the naturally multiscale character of cancer invasion demands appropriate multiscale modelling and analysis approach. The cross-talk between the tissue scale (macro-scale) cancer cell population dynamics and the cell-scale (micro-scale) proteolytic molecular processes along the tumour boundary plays a particularly important role within the invasion processes, leading to dramatic changes in tumour morphology and influencing the overall pattern of cancer spread. Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new formulation of this process involving a novel derivation of the macro-scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells.
Macro
Macro level
Macroscopic scale
Multiscale Modeling
Scale analysis (mathematics)
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Orthotropic material
Macro
Linear elasticity
Macroscopic scale
Elasticity
Representation
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There are two critical issues when deriving a macro-scale prediction model starting from a more complete, underlying model. The first is the precise relationship of the fields predicted by the more complete model and the fields predicted by the macro-scale model. The second is the manner of solving a closure problem that is invariably encountered in all such derivations. The understanding that moving averages of the fields predicted by the more complete model are the fields predicted by the macro-scale model is challenged on the grounds that accomplishing a moving average does not eliminate micro-scale variation, it only appears to do so in one representation of the moving average field. The solution of a closure problem by assumption is challenged on the grounds that the most common assumptions are demonstrably invalid, even while leading to prediction models that can provide reasonable estimates of the macro-scale response in some scenarios. In presenting the challenges, it is further shown how a multiresolution analysis by an orthogonal wavelet system provides a framework for both precisely defining macro-scale response fields, i.e., fields from which all micro-scale variation has been eliminated, and presenting a formally exact solution for a precisely described closure problem.
Macro
Closure (psychology)
Representation
Variation (astronomy)
Scale model
Macroscopic scale
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Macroscopic scale
Macro
Hysteresis
Nanometre
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For estimating the fatigue properties of orthotropic deck bridges, a finite element analysis method was provided. In the method, the models of orthotropic decks steel bridge were established by using Midas and Ansys finite element software respectively, the Midas software has tracked two kinds of live load positions that corresponding to maximum and minimum stress of the fatigue checking points, and the most unfavorable loads were loaded to the Ansys model, then the stress ranges of fatigue checking points were obtained and the fatigue properties of the bridge were estimated. The results show that, it is feasible that using the new finite element method to checking the fatigue performance of orthotropic deck steel bridge.
Orthotropic material
Bridge (graph theory)
Bridge deck
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Central to the quest for a deeper understanding of the cancer growth and spread process, the naturally multiscale character of cancer invasion demands appropriate multiscale modelling and analysis approach. The cross-talk between the tissue scale (macro-scale) cancer cell population dynamics and the cell-scale (micro-scale) proteolytic molecular processes along the tumour boundary plays a particularly important role within the invasion processes, leading to dramatic changes in tumour morphology and influencing the overall pattern of cancer spread.
Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new formulation of this process involving a novel derivation of the macro-scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells.
Macro
Macro level
Macroscopic scale
Multiscale Modeling
Scale analysis (mathematics)
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Orthotropic material
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Citations (88)
Abstract The two‐scale simulation of a linear‐elastic orthotropic disc with a central crack under mode‐I loading may be used to verify the extended finite element method implementation of orthotropic enrichment functions into finite element codes such as FEAP. The stress distribution on the finer scale is simultaneously resolved by the high fidelity generalized method of cells called at each integration point of the macro elements. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Orthotropic material
Macro
High fidelity
Mode (computer interface)
Macroscopic scale
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Composites are multi-scale in nature.The multi-scale simulation stands among one of the most important methods for response analysis of composites,due to its ability to incorporate micro scale damage initiation,evolution and the corresponding effects in macro material property and mechanical behavior.The multi-scale asymptotic expansion theory was used to decompose macro and micro scale governing equation from the original elastic ones,from which the relationship between macro scale and micro scale response was established.Based on synergistic multiscale computational technique,a multi-scale simulation framework was proposed,and development capability provided in commercial finite element software,including user subroutines and scripts were used to implement it.The developed framework can call micro scale model to carry out multi-scale progressive damage simulation during macro model calculation,and information exchange and feedback between macro and micro scale were realized.Micro scale damage model and macro scale phenomenological strength theory can be easily integrated into this multi-scale numerical simulation method with good generality.The tensile simulation example results of carbon/carbon composites shows good agreement with test results.
Macro
Subroutine
Macroscopic scale
Scale analysis (mathematics)
Component (thermodynamics)
Generality
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Бұл зерттеужұмысындaКaно моделітурaлы жәнеоғaн қaтыстытолықмәліметберілгенжәнеуниверситетстуденттерінебaғыттaлғaн қолдaнбaлы (кейстік)зерттеужүргізілген.АхметЯссaуи университетініңстуденттеріүшін Кaно моделіқолдaнылғaн, олaрдың жоғaры білімберусaпaсынa қоятынмaңыздытaлaптaры, яғнисaпaлық қaжеттіліктері,олaрдың мaңыздылығытурaлы жәнесaпaлық қaжеттіліктерінеқaтыстыөз университетінқaлaй бaғaлaйтындығытурaлы сұрaқтaр қойылғaн. Осы зерттеудіңмaқсaты АхметЯсaуи университетіндетуризмменеджментіжәнеқaржы бaкaлaвриaт бaғдaрлaмaлaрыныңсaпaсынa қaтыстыстуденттердіңқaжеттіліктерінaнықтaу, студенттердіңқaнaғaттaну, қaнaғaттaнбaу дәрежелерінбелгілеу,білімберусaпaсын aнықтaу мен жетілдіружолдaрын тaлдaу болыптaбылaды. Осы мaқсaтқaжетуүшін, ең aлдыменКaно сaуaлнaмaсы түзіліп,116 студенткеқолдaнылдыжәнебілімберугежәнеоның сaпaсынa қaтыстыстуденттердіңтaлaптaры мен қaжеттіліктерітоптықжұмыстaрaрқылыaнықтaлды. Екіншіден,бұл aнықтaлғaн тaлaптaр мен қaжеттіліктерКaно бaғaлaу кестесіменжіктелді.Осылaйшa, сaпa тaлaптaры төрт сaнaтқa бөлінді:болуытиіс, бір өлшемді,тaртымдыжәнебейтaрaп.Соңындa,қaнaғaттaну мен қaнaғaттaнбaудың мәндеріесептелдіжәнестуденттердіңқaнaғaттaну мен қaнaғaттaнбaу деңгейлерінжоғaрылaту мен төмендетудеосытaлaптaр мен қaжеттіліктердіңрөліaйқын aнықтaлды.Түйінсөздер:сaпa, сaпaлық қaжеттіліктер,білімберусaпaсы, Кaно моделі.
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