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Computation and experimental comparison of the deformation behavior of pantographic structures with different micro-geometry under shear and torsion

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Additive manufacturing methods, commonly known as 3D printing, allow more sophisticated designs to be created. Willingly designed substructures incorporated into the solid open up new possibilities for uncommon macroscopic deformation behavior. Such a man-made structure is also referred to as a metamaterial. A detailed simulation of a polymer-based metamaterial is challenging but accurately possible by means of the theory of elasticity. In this study, we present experimental investigations of a metamaterial composed of pantographic substructures of different internal geometry. The pantographic structures show an unexpected type of deformation, which can be modeled via elasticity with the aid of direct numerical simulation by using the Finite Element (FE) method. In other words, a detailed mesh is generated involving the substructure. The metamaterial is additively manufactured out of a common polymer showing nonlinear elastic deformation and, therefore, hyperelastic material models are used. Specifically, analytical solutions of a circular cylinder are examined and compared in the case of extension and torsion in order to comprehend the effects of the coefficients inherent to the energy function of the hyperelastic model. Finally, FE computations of pantographic structures are performed and compared with the experimental measurements.
Rocznik
Strony
421--434
Opis fizyczny
Bibliogr. 24 poz., rys., tab.
Twórcy
autor
  • Technische Universität Berlin, Institute of Mechanics, Berlin, Germany
  • Technische Universität Berlin, Institute of Mechanics, Berlin, Germany
Bibliografia
  • 1. Abali B.E., Muller W.H., dell’Isola F., 2017, Theory and computation of higher gradient elasticity theories based on action principles, Archive of Applied Mechanics, 87, 9, 1495-1510
  • 2. Altenbach H., Eremeyev V.A., 2012, Generalized Continua – from the Theory to Engineering Applications, 541, Springer
  • 3. Bahreman M., Darijani H., 2015, New polynomial strain energy function; application to rubbery circular cylinders under finite extension and torsion, Journal of Applied Polymer Science, 132, 13, 41718
  • 4. Barchiesi E., Ganzosch G., Liebold C., Placidi L., Grygoruk R., Muller W.H., 2018a, Out-of-plane buckling of pantographic fabrics in displacement-controlled shear tests: experimental results and model validation, Continuum Mechanics and Thermodynamics, 1-13, DOI: 10.1007/s00161-018-0626-x
  • 5. Barchiesi E., Spagnuolo M., Placidi L., 2018b, Mechanical metamaterials: a state of the art, Mathematics and Mechanics of Solids, 1-23, DOI: 10.1177/1081286517735695
  • 6. Brodecki A., Szymczak T., Kowalewski Z., 2018, Digital image corellation technique as a tool for kinematics assessments of structural components, Acta Mechanica et Automatica, 12, 2, 101-104
  • 7. Chen J.-S., Wu C.-T., 1997, On computational issues in large deformation analysis of rubber bushings, Journal of Structural Mechanics, 25, 3, 287-309
  • 8. Del Vescovo D., Giorgio I., 2014, Dynamic problems for metamaterials: review of existing models and ideas for further research, International Journal of Engineering Science, 80, 153-172
  • 9. Dell’Isola F., Andreaus U., Placidi L., 2014, At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola, Mathematics and Mechanics of Solids, 20, 887-928
  • 10. Dell’Isola F., Giorgio I., Pawlikowski M., Rizzi N.L., 2016, Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium, Proceedings of the Royal Society A, 472, 2185, 1-23
  • 11. Dell’Isola F., Lekszycki T., Pawlikowski M., Grygoruk R., Greco L., 2015, Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence, Zeitschrift f¨ur angewandte Mathematik und Physik, 66, 6, 3473-3498
  • 12. Ganzosch G., dell’Isola F., Turco E., Lekszycki T., Muller W.H. ¨ , 2016, Shearing tests applied to pantographic structures, Acta Polytechnica CTU Proceedings, 7, 1-6
  • 13. Ganzosch G., Hoschke K., Lekszycki T., Giorgio I., Turco E., Muller W.H. ¨ , 2018, 3D- -measurements of 3D-deformations of pantographic structures, Technische Mechanik, 38, 3, 233-245
  • 14. Holzapfel G.A., 2000, Nonlinear Solid Mechanics: a Continuum Approach for Engineering Science, Wiley, Chichester
  • 15. Kowalewski Z.L., Szymczak T., Maciejewski J., 2014, Material effects during monotonic- -cyclic loading, International Journal of Solids and Structures, 51, 3-4, 740-753
  • 16. Lam D., Yang F., Chong A., Wang J., Tong P., 2003, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51, 8, 1477-1508
  • 17. Lawlor M.G., O’Donnell M.R., O’Connell B.M., Walsh M.T., 2011, Experimental determination of circumferential properties of fresh carotid artery plaques, Journal of Biomechanics, 44, 9, 1709-1715
  • 18. Logg A., Mardal K.A., Wells G.N., 2011, Automated solution of differential equations by the finite element method, the FEniCS book, Lecture Notes in Computational Science and Engineering, 84, Springer
  • 19. Mindlin R.D., Eshel N.N., 1968, On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures, 4, 1, 109-124
  • 20. Misra A., Lekszycki T., Giorgio I., Ganzosch G., Muller W.H., dell’Isola F. ¨ , 2018, Pantographic metamaterials show atypical Poynting effect reversal, Mechanics Research Communications, 89, 6-10
  • 21. Rivlin R.S., 1948, Large elastic deformations of isotropic materials. III. Some simple problems in cyclindrical polar co-ordinates, Philosophical Transactions of the Royal Society A, 240, 823, 509-525
  • 22. Thai H.-T., Vo T.P., Nguyen T.-K., Kim S.-E., 2017, A review of continuum mechanics models for size-dependent analysis of beams and plates, Composite Structures, 177, 196219
  • 23. Toupin R.A, 1964, Theories of elasticity with couple-stress, Archive for Rational Mechanics and Analysis, 17, 2, 85112
  • 24. Yang H., Ganzosch G., Giorgio I., Abali B.E., 2018, Material characterization and computations of a polymeric metamaterial with a pantographic substructure, Zeitschrift f¨ur angewandte Mathematik und Physik, 69, 4, 105
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-8ea759a9-87b3-4b03-8094-5b0b02df9adf
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