This paper presents a computationally efficient concurrent multiscale platform to undertake the nonlinear analysis of composite structures. The framework exploits refined one-dimensional models developed within the scheme of the Carrera unified formulation (CUF), which is a generalized hierarchical formulation that generates refined structural theories via a variable kinematic description. The CUF operates at the macro- and microscales, and the macroscale interfaces with a nonlinear micromechanical toolbox. The computational efficiency derives from the ability of the CUF to obtain accurate three-dimensional (3-D)-like stress fields with a reduced computational cost. The nonlinearity is at the matrix level within the microscale, and its effect scales up to the macroscale through homogenization. The macrotangent matrix adopts a perturbation-based method to have meliorated performances. The numerical results demonstrate that the framework requires some 50% of the computational time and 10% of memory usage of traditional 3-D finite elements. Very detailed local effects at the microscale are detectable, and there are no restrictions concerning the complexity of the geometry.

References

[1] Liu X., Furrer D., Kosters J. and Holmes J., “Vision 2040: A Roadmap for Integrated, Multiscale Modeling and Simulation of Materials and Systems,” NASA John H. Glenn Research Center NTRS Document ID: 20180002010, Cleveland, OH, 2018, https://ntrs.nasa.gov/search.jsp?R=20180002010. Google Scholar
[2] Aboudi J., Arnold S. and Bednarcyk B., Micromechanics of Composite Materials, Elsevier, New York, 2012, pp. 12–15. doi:https://doi.org/10.1016/C2011-0-05224-9 Google Scholar
[3] Herakovich C. T., Mechanics of Fibrous Composites, Wiley, New York, 1997. doi:https://doi.org/10.1016/C2011-0-05224-9. Google Scholar
[4] Hashin Z. and Rosen B. W., “The Elastic Moduli of Fiber-Reinforced Materials,” Journal of Applied Mechanics, Vol. 31, No. 2, 1964, pp. 223–232, 412–446. doi:https://doi.org/10.1115/1.3629590. Crossref Google Scholar
[5] Mori T. and Tanaka K., “Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions,” Acta Metallurgica, Vol. 21, No. 5, 1973, pp. 571–574. doi:https://doi.org/10.1016/0001-6160(73)90064-3. Crossref Google Scholar
[6] Huang Y., Hu K., Wei X. and Chandra A., “A Generalized Self-Consistent Mechanics Method for Composite Materials with Multiphase Inclusions,” Journal of the Mechanics and Physics of Solids, Vol. 42, No. 3, 1994, pp. 491–504. doi:https://doi.org/10.1016/0022-5096(94)90028-0. Crossref Google Scholar
[7] Segurado J., Llorca J. and González C., “On the Accuracy of Mean-Field Approaches to Simulate the Plastic Deformation of Composites,” Scripta Materialia, Vol. 46, No. 7, 2002, pp. 525–529. doi:https://doi.org/10.1016/S1359-6462(02)00027-1. Crossref Google Scholar
[8] Zhang D. and Waas A. M., “A Micromechanics Based Multiscale Model for Nonlinear Composites,” Acta Mechanica, Vol. 225, No. 4, 2014, pp. 1391–1417. doi:https://doi.org/10.1007/s00707-013-1057-1 Crossref Google Scholar
[9] Patel D. and Waas A., “Damage and Failure Modelling of Hybrid Three-Dimensional Textile Composites: A Mesh Objective Multi-Scale Approach,” Philosophical Transactions of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Vol. 374, No. 2071, 2017. doi:https://doi.org/10.1098/rsta.2016.0036. Google Scholar
[10] Zhang D., Patel D. K. and Waas A. M., “A Novel Two-Scale Progressive Failure Analysis Method for Laminated Fiber-Reinforced Composites,” 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2015-0969, Jan. 2015, pp. 1–19. doi:https://doi.org/10.2514/6.2015-0969. Link Google Scholar
[11] Zhang D., Waas A. M. and Yen C. F., “Progressive Damage and Failure Response of Hybrid 3-D Textile Composites Subjected to Flexural Loading, Part II: Mechanics Based Multiscale Computational Modeling of Progressive Damage and Failure,” International Journal of Solids and Structures, Vols. 75–76, Dec. 2015, pp. 321–335. doi:https://doi.org/10.1016/j.ijsolstr.2015.06.033. Crossref Google Scholar
[12] Digimat, Software Package, Digimat 6.1.1, e-Xstream Engineering, Louvain-la-Neuve, Belgium, 2018. Google Scholar
[13] Paley M. and Aboudi J., “Micromechanical Analysis of Composites by the Generalized Cells Model,” Mechanics of Materials, Vol. 14, No. 2, 1992, pp. 127–139. doi:https://doi.org/10.1016/0167-6636(92)90010-B. Crossref Google Scholar
[14] Aboudi J., Pindera M.-J. and Arnold S., “Higher-Order Theory for Functionally Graded Materials,” Composites Part B: Engineering, Vol. 30, No. 8, 1999, pp. 777–832. doi:https://doi.org/10.1016/S1359-8368(99)00053-0. Crossref Google Scholar
[15] Pineda E. J., Waas A. M., Bednarcyk B. A., Collier C. S. and Yarrington P. W., “Progressive Damage and Failure Modeling in Notched Laminated Fiber Reinforced Composites,” International Journal of Fracture, Vol. 158, No. 2, 2009, pp. 125–143. doi:https://doi.org/10.1007/s10704-009-9370-3. Crossref Google Scholar
[16] Naghipour P., Arnold S. M., Pineda E. J., Stier B., Hansen L., Bednarcyk B. A. and Waas A. M., “Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells,” Journal of Composite Materials, Vol. 51, No. 10, 2017, pp. 1433–1454. doi:https://doi.org/10.1177/0021998316651708. Crossref Google Scholar
[17] Haj-Ali R. and Aboudi J., “Nonlinear Micromechanical Formulation of the High Fidelity Generalized Method of Cells,” International Journal of Solids and Structures, Vol. 46, No. 13, 2009, pp. 2577–2592. doi:https://doi.org/10.1016/j.ijsolstr.2009.02.004. Crossref Google Scholar
[18] Ricks T. M., Lacy T. E., Pineda E. J., Bednarcyk B. A. and Arnold S. M., “Computationally Efficient High-Fidelity Generalized Method of Cells Micromechanics via Order-Reduction Techniques,” Composite Structures, Vol. 156, Nov. 2016, pp. 2–9. doi:https://doi.org/10.1016/j.compstruct.2016.05.093. Crossref Google Scholar
[19] Feyel F., “Multiscale FE² Elastoviscoplastic Analysis of Composite Structures,” Computational Materials Science, Vol. 16, No. 1, 1999, pp. 344–354. doi:https://doi.org/10.1016/S0927-0256(99)00077-4. Crossref Google Scholar
[20] Meyer P. and Waas A. M., “Mesh-Objective Two-Scale Finite Element Analysis of Damage and Failure in Ceramic Matrix Composites,” Integrating Materials and Manufacturing Innovation, Vol. 4, No. 1, 2015, Paper 18. doi:https://doi.org/10.1186/s40192-015-0034-z. Crossref Google Scholar
[21] Tikarrouchine E., Chatzigeorgiou G., Praud F., Piotrowski B., Chemisky Y. and Meraghni F., “Three-Dimensional FE² Method for the Simulation of Non-Linear, Rate-Dependent Response of Composite Structures,” Composite Structures, Vol. 193, June 2018, pp. 165–179. doi:https://doi.org/10.1016/j.compstruct.2018.03.072. Crossref Google Scholar
[22] Verhoosel C. V., Remmers J. J. C., Gutiérrez M. A. and de Borst R., “Computational Homogenization for Adhesive and Cohesive Failure in Quasi-Brittle Solids,” International Journal for Numerical Methods in Engineering, Vol. 83, Nos. 8–9, 2010, pp. 1155–1179. doi:https://doi.org/10.1002/nme.2854. Crossref Google Scholar
[23] Feyel F. and Chaboche J. L., “FE² Multiscale Approach for Modelling the Elastoviscoplastic Behaviour of Long Fibre SiC/Ti Composite Materials,” Computer Methods in Applied Mechanics and Engineering, Vol. 183, No. 3, 2000, pp. 309–330. doi:https://doi.org/10.1016/S0045-7825(99)00224-8. Crossref Google Scholar
[24] Chinesta F., Ammar A. and Cueto E., “Recent Advances and New Challenges in the Use of the Proper Generalized Decomposition for Solving Multidimensional Models,” Archives of Computational Methods in Engineering, Vol. 17, No. 4, 2010, pp. 327–350. doi:https://doi.org/10.1007/s11831-010-9049-y. Crossref Google Scholar
[25] Néron D. and Ladevèze P., “Proper Generalized Decomposition for Multiscale and Multiphysics Problems,” Archives of Computational Methods in Engineering, Vol. 17, No. 4, 2010, pp. 351–372. doi:https://doi.org/10.1007/s11831-010-9053-2. Crossref Google Scholar
[26] Radermacher A., Bednarcyk B., Stier B., Simon J., Zhou L. and Reese S., “Displacement-Based Multiscale Modeling of Fiber-Reinforced Composites by Means of Proper Orthogonal Decomposition,” Advanced Modeling and Simulation in Engineering Sciences, Vol. 3, No. 1, 2016, p. 29. doi:https://doi.org/10.1186/s40323-016-0082-8. Crossref Google Scholar
[27] Kanouté P., Boso D. P., Chaboche J. L. and Schrefler B. A., “Multiscale Methods for Composites: A Review,” Archives of Computational Methods in Engineering, Vol. 16, No. 1, 2009, pp. 31–75. doi:https://doi.org/10.1007/s11831-008-9028-8. Crossref Google Scholar
[28] Carrera E., Cinefra M., Zappino E. and Petrolo M., Finite Element Analysis of Structures Through Unified Formulation, Wiley, Hoboken, NJ, 2014, pp. 151–170. doi:https://doi.org/10.1002/9781118536643. Crossref Google Scholar
[29] Kaleel I., Petrolo M., Waas A. M. and Carrera E., “Micromechanical Progressive Failure Analysis of Fiber- Reinforced Composite Using Refined Beam Models,” Journal of Applied Mechanics, Vol. 85, Feb. 2018, pp. 1–8. doi:https://doi.org/10.1115/1.4038610. Google Scholar
[30] Pagani A. and Carrera E., “Large-Deflection and Post-Buckling Analyses of Laminated Composite Beams by Carrera Unified Formulation,” Composite Structures, Vol. 170, March 2017, pp. 40–52. doi:https://doi.org/10.1016/j.compstruct.2017.03.008. Crossref Google Scholar
[31] Carrera E., Guarnera D. and Pagani A., “Static and Free-Vibration Analyses of Dental Prosthesis and Atherosclerotic Human Artery by Refined Finite Element Models,” Biomechanics and Modeling in Mechanobiology, Vol. 17, No. 2, 2018, pp. 301–317. doi:https://doi.org/10.1007/s10237-017-0961-z. Crossref Google Scholar
[32] Petrolo M., Nagaraj M., Kaleel I. and Carrera E., “A Global-Local Approach for the Elastoplastic Analysis of Compact and Thin-Walled Structures via Refined Models,” Computers and Structures, Vol. 206, June 2018, pp. 54–65. doi:https://doi.org/10.1016/j.compstruc.2018.06.004. Crossref Google Scholar
[33] Kaleel I., Petrolo M., Waas A. and Carrera E., “Computationally Efficient, High-Fidelity Micromechanics Framework Using Refined 1-D Models,” Composite Structures, Vol. 181, Aug. 2017, pp. 358–367. doi:https://doi.org/10.1016/j.compstruct.2017.08.040. Crossref Google Scholar
[34] Miehe C., “Numerical Computation of Algorithmic (Consistent) Tangent Moduli in Large-Strain Computational Inelasticity,” Computer Methods in Applied Mechanics and Engineering, Vol. 134, No. 3, 1996, pp. 223–240. doi:https://doi.org/10.1016/0045-7825(96)01019-5. Crossref Google Scholar
[35] Carrera E. and Petrolo M., “Refined Beam Elements with only Displacement Variables and Plate/Shell Capabilities,” Meccanica, Vol. 47, No. 3, 2011, pp. 537–556. doi:https://doi.org/10.1007/s11012-011-9466-5. Crossref Google Scholar
[36] Carrera E., Kaleel I. and Petrolo M., “Elastoplastic Analysis of Compact and Thin-Walled Structures Using Classical and Refined Beam Finite Element Models,” Mechanics of Advanced Materials and Structures, Vol. 26, No. 3, Oct. 2017, pp. 274–286. doi:https://doi.org/10.1080/15376494.2017.1378780. Crossref Google Scholar
[37] Sun C. and Joon Y. K., “Elastic-Plastic Analysis of AS4/PEEK Composite Laminate Using a One-Parameter Plasticity Model,” Journal of Composite Materials, Vol. 26, No. 2, 1992, pp. 293–308. doi:https://doi.org/10.1177/002199839202600208. Crossref Google Scholar
[38] Vogler M., Rolfes R. and Camanho P. P., “Mechanics of Materials Modeling the Inelastic Deformation and Fracture of Polymer Composites—Part I: Plasticity Model,” Mechanics of Materials, Vol. 59, April 2013, pp. 50–64. doi:https://doi.org/10.1016/j.mechmat.2012.12.002. Crossref Google Scholar
[39] von Mises R., “Mechanics of Solid Bodies in the Plastically-Deformable State,” Mechanik der Festen Körper in Plastisch-Deformablen Zustand, Vol. 4, 1913, pp. 582–592. Google Scholar
[40] Kouznetsova V., Brekelmans W. A. M. and Baaijens F. P. T., “An Approach to Micro-Macro Modeling of Heterogeneous Materials,” Computational Mechanics, Vol. 27, No. 1, 2001, pp. 37–48. doi:https://doi.org/10.1007/s004660000212. Crossref Google Scholar
[41] Miehe C. and Koch A., “Computational Micro-to-Macro Transitions of Discretized Microstructures Undergoing Small Strains,” Archive of Applied Mechanics, Vol. 72, No. 4, 2002, pp. 300–317. doi:https://doi.org/10.1007/s00419-002-0212-2. Crossref Google Scholar
[42] Geers M. G., Kouznetsova V. G., Matouš K. and Yvonnet J., Homogenization Methods and Multiscale Modeling: Nonlinear Problems, American Cancer Soc., 2017, pp. 1–34. doi:https://doi.org/10.1002/9781119176817.ecm2107. Google Scholar
[43] Spahn J., Andrä H., Kabel M. and Müller R., “A Multiscale Approach for Modeling Progressive Damage of Composite Materials Using Fast Fourier Transforms,” Computer Methods in Applied Mechanics and Engineering, Vol. 268, Jan. 2014, pp. 871–883. doi:https://doi.org/10.1016/j.cma.2013.10.017. Crossref Google Scholar
[44] Dagum L. and Menon R., “OpenMP: An Industry-Standard API for Shared-Memory Programming,” IEEE Computing in Science and Engineering, Vol. 5, No. 1, 1998, pp. 46–55. doi:https://doi.org/10.1109/99.660313. Crossref Google Scholar
[45] O'Higgins R., “An Experimental and Numerical Study of Damage Initiation and Growth in High Strength Glass and Carbon Fiber-Reinforced Composite Materials,” Ph.D. Thesis, Univ. of Limerick, Limerick, Ireland, 2007. Google Scholar
[46] O’Higgins R., McCarthy C. T. and McCarthy M. A., “Effects of Shear-Transverse Coupling and Plasticity in the Formulation of an Elementary Ply Composites Damage Model, Part I: Model Formulation and Validation,” Strain, Vol. 48, No. 1, 2012, pp. 49–58. doi:https://doi.org/10.1111/j.1475-1305.2010.00797.x. Crossref Google Scholar
[47] Kaleel I., Petrolo M. and Carrera E., “Elastoplastic and Progressive Failure Analysis of Fiber-Reinforced Composites via an Efficient Nonlinear Microscale Model,” Aerotecnica Missili and Spazio, Vol. 97, No. 2, 2018, pp. 103–110. doi:https://doi.org/10.1007/BF03405805. Crossref Google Scholar

Volume 57, Number 9September 2019

Special Section on Advances in Bio-inspired Propulsion

Crossmark

Information

Copyright © 2019 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-385X to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp.

Topics

Keywords

Acknowledgments

This research work has been carried out within the project FULLCOMP (which stands for Fully Analysis, Design, Manufacturing, and Health Monitoring Of Composite Structures), which is funded by the European Union Horizon 2020 Research and Innovation program under the Marie Skłodowska-Curie grant agreement no. 642121. The uthors would also like to acknowledge the computational resources provided by High Performance Computing @ POLITO ([email protected]).

Received18 September 2018
Accepted1 June 2019
Published online3 July 2019

Computationally Efficient Concurrent Multiscale Framework for the Nonlinear Analysis of Composite Structures

Abstract

References

What's Popular

Information