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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 7
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Original Articles

Three-scale convergence for processes in heterogeneous media

D. Trucu Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UKCorrespondence[email protected]
,
M.A.J. Chaplain Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK
&
A. Marciniak-Czochra Interdisciplinary Center of Scientific Computing and BIOQUANT, University of Heidelberg, Im Neuenheimer Feld 267, 69120, Heidelberg, Germany
Pages 1351-1373 | Received 21 Sep 2010, Accepted 02 Mar 2011, Published online: 15 Apr 2011

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Oscar Luis Cruz-González, Ariel Ramírez-Torres, Reinaldo Rodríguez-Ramos, Raimondo Penta, Julián Bravo-Castillero, Raúl Guinovart-Díaz, José Merodio, Federico J. Sabina & Frederic Lebon. (2021) A hierarchical asymptotic homogenization approach for viscoelastic composites. Mechanics of Advanced Materials and Structures 28:21, pages 2190-2201.
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Articles from other publishers (28)

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O.L. Cruz-González, A. Ramírez-Torres, R. Rodríguez-Ramos, R. Penta & F. Lebon. (2022) Hierarchical heterogeneous one-dimensional problem in linear viscoelastic media. European Journal of Mechanics - A/Solids 95, pages 104617.
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Hao Dong. (2022) Computationally efficient higher-order three-scale method for nonlocal gradient elasticity problems of heterogeneous structures with multiple spatial scales. Applied Mathematical Modelling 109, pages 426-454.
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Hao Dong, Junzhi Cui, Yufeng Nie, Ke Jin, Xiaofei Guan & Zihao Yang. (2020) High-order three-scale computational method for elastic behavior analysis and strength prediction of axisymmetric composite structures with multiple spatial scales. Mathematics and Mechanics of Solids 26:6, pages 905-936.
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Qiang Ma, Shuyu Ye, Junzhi Cui, Zhiqiang Yang, Xue Jiang & Zhihui Li. (2021) Two-scale and three-scale asymptotic computations of the Neumann-type eigenvalue problems for hierarchically perforated materials. Applied Mathematical Modelling 92, pages 565-593.
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Zhiqiang Yang, Yi Sun, Junzhi Cui & Qiang Ma. (2021) A high-order three-scale reduced homogenization for nonlinear heterogeneous materials with multiple configurations. Journal of Computational Physics 425, pages 109900.
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Zhiqiang Yang, Yi Sun, Tianyu Guan & Hao Dong. (2020) A high-order three-scale approach for predicting thermo-mechanical properties of porous materials with interior surface radiation. Computers & Mathematics with Applications 79:9, pages 2742-2770.
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Ariel Ramírez-Torres, Raimondo Penta, Reinaldo Rodríguez-Ramos & Alfio Grillo. (2019) Effective properties of hierarchical fiber-reinforced composites via a three-scale asymptotic homogenization approach. Mathematics and Mechanics of Solids 24:11, pages 3554-3574.
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Vasiliy Grigoriev, Petr Zakharov & Mir Akimov. (2019) Effective calculation of thermophysical properties of composite materials with multiple configurations by asymptotic homogenization technique. Journal of Physics: Conference Series 1392:1, pages 012069.
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Eduard Rohan, Jana Turjanicová & Vladimír Lukeš. (2019) The Biot–Darcy–Brinkman model of flow in deformable double porous media; homogenization and numerical modelling. Computers & Mathematics with Applications 78:9, pages 3044-3066.
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Hao Dong, Xiaojing Zheng, Junzhi Cui, Yufeng Nie, Zhiqiang Yang & Zihao Yang. (2019) High-order three-scale computational method for dynamic thermo-mechanical problems of composite structures with multiple spatial scales. International Journal of Solids and Structures 169, pages 95-121.
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Ariel Ramírez-Torres, Raimondo Penta, Reinaldo Rodríguez-Ramos, Alfio Grillo, Luigi Preziosi, José Merodio, Raúl Guinovart-Díaz & Julián Bravo-Castillero. (2018) Homogenized out-of-plane shear response of three-scale fiber-reinforced composites. Computing and Visualization in Science 20:3-6, pages 85-93.
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Zhiqiang Yang, Yi Sun, Junzhi Cui & Jingran Ge. (2019) A three-scale asymptotic expansion for predicting viscoelastic properties of composites with multiple configuration. European Journal of Mechanics - A/Solids 76, pages 235-246.
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Zhiqiang Yang, Yi Sun, Yizhi Liu, Tianyu Guan & Hao Dong. (2019) A three-scale asymptotic analysis for ageing linear viscoelastic problems of composites with multiple configurations. Applied Mathematical Modelling 71, pages 223-242.
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Zhiqiang Yang, Yi Sun, Junzhi Cui, Zihao Yang & Tianyu Guan. (2018) A three-scale homogenization algorithm for coupled conduction-radiation problems in porous materials with multiple configurations. International Journal of Heat and Mass Transfer 125, pages 1196-1211.
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Eduard Rohan, Jana Turjanicová & Vladimír Lukeš. (2018) A Darcy-Brinkman model of flow in double porous media – Two-level homogenization and computational modelling. Computers & Structures 207, pages 95-110.
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Hao Dong, Junzhi Cui, Yufeng Nie, Zihao Yang & Ziqiang Wang. (2018) High-order three-scale computational method for heat conduction problems of axisymmetric composite structures with multiple spatial scales. Advances in Engineering Software 121, pages 1-12.
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Ariel Ramírez-Torres, Raimondo Penta, Reinaldo Rodríguez-Ramos, José Merodio, Federico J. Sabina, Julián Bravo-Castillero, Raúl Guinovart-Díaz, Luigi Preziosi & Alfio Grillo. (2018) Three scales asymptotic homogenization and its application to layered hierarchical hard tissues. International Journal of Solids and Structures 130-131, pages 190-198.
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Zihao Yang, Yang Zhang, Hao Dong, Junzhi Cui, Xiaofei Guan & Zhiqiang Yang. (2017) High-order three-scale method for mechanical behavior analysis of composite structures with multiple periodic configurations. Composites Science and Technology 152, pages 198-210.
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Lu Peng, Dumitru Trucu, Ping Lin, Alastair Thompson & Mark A. J. Chaplain. (2017) A Multiscale Mathematical Model of Tumour Invasive Growth. Bulletin of Mathematical Biology 79:3, pages 389-429.
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Dumitru Trucu & Mark A. J. Chaplain. 2014. Managing Complexity, Reducing Perplexity. Managing Complexity, Reducing Perplexity 45 53 .
Dumitru Trucu, Ping Lin, Mark A. J. Chaplain & Yangfan Wang. (2013) A Multiscale Moving Boundary Model Arising in Cancer Invasion. Multiscale Modeling & Simulation 11:1, pages 309-335.
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Hao Dong, Zihao Yang, Xiaofei Guan & Junzhi Cui. (2022) Stochastic Higher-Order Three-Scale Strength Prediction Model for Composite Structures with Micromechanical Analysis. SSRN Electronic Journal.
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