152
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A Large Strains Finite Element Multiscale Approach

&

References

  • D. Peric, E.A. De Souza Neto, R.A. Feijo, M. Partovi, and A.J.C. Molina, On Micro-to-Macro Transitions for Multi-Scale Analysis of Non-Linear Heterogeneous Materials: Unified Variational Basis and Finite Element Implementation, Int. J. Numer. Method Eng., vol. 87, no. 1–5, pp. 149–170, 2011.
  • C. Miehe, J. Schotte, and J. Schroder, Computational Micro-Macro Transitions and Overall Tangent Moduli in the Analysis of Polycrystals at Large Strains, Comput. Mater. Sci., vol. 16, pp. 372–382, 1999.
  • C. Miehe and A. Koch, Computational Micro-to-Macro Transitions of Discretized Microstructures Undergoing Small Strains, Arch. Appl. Mech., vol. 72, pp. 300–317, 2002.
  • C.W. Miehe and D.R. Clarke, The Influence of Particle Size and Particle Fracture o the Elastic/Plastic Deformation of Metal Matrix Composite, Acta Mater., vol. 44, no. 9, pp. 3801–3811, 1996.
  • V.G. Kouznetsova, W.A.M. Brekelmans, and F.P.T. Baaijens, An Approach to Micro-Macro Modelling of Heterogeneous Materials, Comput. Mech., vol. 27, pp. 37–48, 2001.
  • A.J. Carneiro Molina and J.L. Curiel-Sosa, A Multiscale Finite Element Technique for Nonlinear Multiphase Materials, Finit. Elem. Anal. Des., vol. 94, pp. 64–80, 2015.
  • C. Reina, B. Li, K. Weinberg, and M. Ortiz, A Micromechanical Model of Distributed Damage Due to Void Growth in General Materials and Under General Deformationhistories, Int. J. Numer. Method. Eng., vol. 93, no. 6, pp. 575–611, 2013.
  • Y. Aoyagi and K. Shizawa, A Dislocation-Crystal Plasticity Simulation on Large Deformation Considering Geometrically Necessary Dislocation Density and Incompatibility (2nd Report, Application to fcc Single Crystal), Nihon Kikai Gakkai Ronbunshu, A Hen/Trans. Japan Soc. Mech. Eng., Part A, vol. 72, no. 11, pp. 1646–1653, 2006.
  • M. Kastner, G. Haasemann, and V. Ulbricht, Multiscale xfem-Modelling and Simulation of the Inelastic Material Behaviour of Textile-Reinforced Polymers, Int. J. Numer. Meth. Eng., vol. 86, no. 4-5, pp. 477–498, 2011.
  • I. Watanabe, D. Setoyama, N. Nagasako, N. Iwata, and K. Nakanishi, Multiscale Prediction of Mechanical Behavior of Ferrite-Pearlite Steel With Numerical Material Testing, Int. J. Numer. Meth. Eng., vol. 89, no. 7, pp. 829–845, 2012.
  • I.M. Gitman, Representative Volumes and Multi-Scale Modelling of Quasi-Brittle Materials, PhD thesis, Technische Universiteit Delft, 2006.
  • O. Lloberas-Valls, D.J. Rixen, A. Simone, and L.J. Sluys, Multiscale Domain Decomposition Analysis of Quasi-Brittle Heterogeneous Materials, Int. J. Numer. Meth. Eng., vol. 89, no. 11, pp. 1337–1366, 2012.
  • V.P. Nguyen, O. Lloberas-Valls, M. Stroeven, and L.J. Sluys, Computational Homogenization for Multiscale Crack Modeling. Implementational and Computational Aspects, Int. J. Numer. Meth. Eng., vol. 89, no. 2, pp. 192–226, 2012.
  • C. Oskay, Two-Level Multiscale Enrichment Methodology for Modeling of Heterogeneous Plates, Int. J. Numer. Meth. Eng., vol. 80, no. 9, pp. 1143–1170, 2009.
  • P. Ladeveze, Multiscale Modelling and Computational Strategies for Composites, Int. J. Numer. Meth. Eng., vol. 60, no. 1, pp. 233–253, 2004.
  • B.N. Nguyen and K.L. Simmons, A Multiscale Modeling Approach to Analyze Filament-Wound Composite Pressure Vessels, J. Compos. Mater., vol. 47, no. 17, pp. 2113–2123, 2013.
  • S. Marfia and E. Sacco, Analysis of sma Composite Laminates Using a Multiscale Modelling Technique, Int. J. Numer. Meth. Eng., vol. 70, no. 10, pp. 1182–1208, 2007.
  • S. Torquato, Random Heterogeneous Materials. Microestructure and Macroscopic Properties, Springer, New York, 2002.
  • F.J. Vernerey and M. Kabiri, Adaptive Concurrent Multiscale Model for Fracture and Crack Propagation in Heterogeneous Media, Comput. Method. Appl. Mech. Eng., vol. 276, pp. 566–588, 2014.
  • V. Peron-Luhrs, F. Sansoz, A. Jrusalem, and L. Noels, Multiscale Computational Modeling of Deformation Mechanics and Intergranular Fracture in Nanocrystalline Copper, Comput. Mater. Sci., vol. 90, pp. 253–264, 2014.
  • M. Kabiri and F.J. Vernerey, An xfem Based Multiscale Approach to Fracture of Heterogeneous Media, Int. J. Multiscale Comput. Eng., vol. 11, no. 6, pp. 565–580, 2013.
  • N. Zhang, J. Yao, Z. Huang, and Y. Wang, Accurate Multiscale Finite Element Method for Numerical Simulation of Two-Phase Flow in Fractured Media Using Discrete-Fracture Model, J. Comput. Phys., vol. 242, pp. 420–438, 2013.
  • R.A. Regueiro and S.-K. Yu, Finite-Element Analysis of Grain-Matrix Micro-Cracking in Shale Within the Context of a Multiscale Modeling Approach for Fracture, Int. J. Multiscale Comput. Eng., vol. 10, no. 5, pp. 407–424, 2012.
  • C.V. Verhoosel, J.J.C. Remmers, and M.A. Gutirrez, A Partition of Unity-Based Multiscale Approach for Modelling Fracture in Piezoelectric Ceramics, Int. J. Numer. Meth. Eng., vol. 82, no. 8, pp. 966–994, 2010.
  • C. Gonzalez and J. Llorca, Multiscale Modeling of Fracture in Fiber-Reinforced Composites, Acta Mater., vol. 54, no. 16, pp. 4171–4181, 2006.
  • C. Miehe and J. Dettmar, A Framework for Micro-Macro Transitions in Periodic Particle Aggregates of Granular Materials, Comput. Method. Appl. Mech. Eng., vol. 193, pp. 225–256, 2004.
  • E. W.C. Coenen, V.G. Kouznetsova, and M. G.D. Geers, Computational Homogenization for Heterogeneous Thin Sheets, Int. J. Numer. Meth. Eng., vol. 83, no. 8-9, pp. 1180–1205, 2010.
  • V.K. Lai, M.F. Hadi, R.T. Tranquillo, and V.H. Barocas, A Multiscale Approach to Modeling the Passive Mechanical Contribution of Cells in Tissues, J. Biomech. Eng., vol. 135, no. 7, 2013.
  • M. Marino and G. Vairo, Stress and Strain Localization in Stretched Collagenous Tissues via a Multiscale Modelling Approach, Comput. Method. Biomech. Biomed. Eng., vol. 17, no. 1, pp. 11–30, 2014.
  • A. Abdulle, On a Priori Error Analysis of Fully Discrete Heterogeneous Multiscale Fem, Multiscale Model. Simulat., vol. 4, no. 2, pp. 447–459, 2005.
  • R. Tian, A.C. To, and W.K. Liu, Conforming Local Meshfree Method, Int. J. Numer. Meth. Eng., vol. 86, no. 3, pp. 335–357, 2011.
  • C. Miehe, Computational Micro-to-Macro Transitions for Discretized Micro-Structures of Heterogeneous Materials at Finite Strains Based on the Minimization of Averaged Incremental Energy, Comput. Method. Appl. Mech. Eng., vol. 192, pp. 559–591, 2003.
  • R. Hill, On Constitutive Macro-Variables for Heterogeneous Solids at Finite Strain, Proc. R. Soc. London, vol. 326, pp. 131–147, 1972.
  • C. Miehe, J. Schroder, and Computational Homogenization Analysis in Finite Plasticity. Simulation of Texture Development in Polycrystalline Materials, Comput. Method. Appl. Mech. Eng., vol. 171, pp. 387–418, 1999.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.