A new look at periodic homogenization methods towards generalized continua and applications to architectured materials - presented by Prof. Jean-Francois Ganghoffer

A new look at periodic homogenization methods towards generalized continua and applications to architectured materials

Prof. Jean-Francois Ganghoffer

JG
Slide at 05:45
Scientific issues of higher order homogenizatio jean-françois gangh.. Specific theoretical & numerical difficulties compared to higher gradient theories: Emergence of new degrees of freedom at macroscale (absent at microscale) A priori Ansatz for the static and kinematic variables [9], [10] Size-dependency of higher-order moduli [12] Non-zero higher-order moduli for homogeneous domains [13] Surface formulation of higher-order static and kinematic variables [11] Numerical schemes to compute effective higher-order properties [14] [9] Biswas, R., Poh, L. H., & Shedbale, A. S., (2020), Journal of the Mechanics and Physics of Solids. [10] Hütter, G., Mühlich, U., & Kuna, M., (2015), Continuum Mechanics and Thermodynamics. Hütter, am 2019. J. Mech. Phys. Solids 127, 62-79. https://doi.org/10.1016/j.jmps.2019.03.005 [11] Caillerie, D., (2012), Ecole d'été "Méthodes asymptotiques en mécanique" Quiberon septembre. [12] Barboura, S., & Li, J., (2018), International Journal of Solids and Structures. [13] Forest, S., & Trinh, D. K., (2011), ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik. [14] Omairey, S. L., Dunning, P. D., & Sriramula, S., (2019), Engineering with Computers. [15] Tekoglu, C., Gibson, LJ, & Onck, P., (2011), In Tessellations in the Sciences: Virtues, Techniques and Applications of Geometric Tilings. [16] Yang, H., & Müller, W. H., (2021), Archive of Applied Mechanics. [17] Andrianov, I. V., Awrejcewicz, J., & Diskovsky, A. A., 2006, Journal of Vibration and Acoustics.
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References
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    R. Biswas et al. (2019) A micromorphic computational homogenization framework for auxetic tetra-chiral structures. Journal of the Mechanics and Physics of Solids
  • 2.
    G. Hütter et al. (2014) Micromorphic homogenization of a porous medium: elastic behavior and quasi-brittle damage. Continuum Mechanics and Thermodynamics
  • 3.
    Caill\u00e9ne, D., (2012), Ecole d\u2019\u00e9t\u00e9 \u00abM\u00e9thodes asymptotiques en m\u00e9canique\u00bb Quiberon septembre.
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    G. Hütter (2019) On the micro-macro relation for the microdeformation in the homogenization towards micromorphic and micropolar continua. Journal of the Mechanics and Physics of Solids
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    S. Barboura and J. Li (2017) Establishment of strain gradient constitutive relations by using asymptotic analysis and the finite element method for complex periodic microstructures. International Journal of Solids and Structures
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    S. Forest and D. K. Trinh (2010) Generalized continua and non‐homogeneous boundary conditions in homogenisation methods. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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    S. L. Omairey et al. (2018) Development of an ABAQUS plugin tool for periodic RVE homogenisation. Engineering with Computers
  • 8.
    https://research.rug.nl/en/publications/size-effects-of-metal-foams
  • 9.
    H. Yang and W. H. Müller (2020) Size effects of mechanical metamaterials: a computational study based on a second-order asymptotic homogenization method. Archive of Applied Mechanics (Ingenieur Archiv)
  • 10.
    I. V. Andrianov et al. (2006) Homogenization of Quasi-Periodic Structures. Journal of Vibration and Acoustics
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