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Microstructural Statistics Informed Boundary Conditions for Statistically Equivalent Representative Volume Elements (SERVEs) of Polydispersed Elastic Composites

  • Somnath GhoshEmail author
  • Dhirendra V. Kubair
  • Craig Przybyla
Chapter
  • 43 Downloads

Abstract

The statistically equivalent RVE or P-SERVE have been introduced in Swaminathan et al. (J Compos Mater 40(7):583–604, 2006) and Ghosh (Micromechanical analysis and multi-scale modeling using the voronoi cell finite element method. CRC Press/Taylor & Francis, Boca Raton, 2011) as the smallest microstructural volume element in non-uniform microstructures that has effective material properties equivalent to those of the entire microstructure. An important consideration is the application of appropriate boundary conditions for optimal SERVE domains. The exterior statistics-based boundary conditions or ESBCs have been developed in Ghosh and Kubair (J Mech Phys Solids 96:1–24, 2016), Kubair and Ghosh (Int J Solids Struct 112:106–121, 2017), Kubair et al. (J Comput Mech 52(21):2919–2928, 2018), accounting for the statistics of fiber distributions and interactions in the domain exterior to the SERVE. The ESBC-based SERVEs have been validated for effective convergence in evaluating homogenized stiffnesses and optimal domains for micromechanical analysis. Validation is also conducted with an experimentally studied carbon-fiber epoxy-matrix polymer matrix composite (PMC). The performance of the SERVE with ESBCs is compared with other boundary conditions, as well as with the statistical volume elements (SVE). The tests clearly show the significant advantages of the ESBCs in terms of accuracy of the homogenized stiffness and efficiency.

Keywords

Polymer matrix composite (PMC) Exterior statistics-based boundary conditions (ESBCs) Statistically equivalent RVE or SERVE Micromechanical analysis 

Notes

Acknowledgements

This work has been supported through a grant No. FA9550-12-1-0445 to the Center of Excellence on Integrated Materials Modeling (CEIMM) at Johns Hopkins University awarded by the AFOSR/RSL Computational Mathematics Program (Manager Dr. A. Sayir) and AFRL/RX (Monitors Drs. C. Woodward and C. Przybyla). These sponsorships are gratefully acknowledged. Computing support by the Homewood High-Performance Compute Cluster (HHPC) and Maryland Advanced Research Computing Center (MARCC) is gratefully acknowledged.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Somnath Ghosh
    • 1
    Email author
  • Dhirendra V. Kubair
    • 2
  • Craig Przybyla
    • 3
  1. 1.Departments of Civil, Mechanical Engineering and Materials Science & EngineeringJohns Hopkins UniversityBaltimoreUSA
  2. 2.Department of Civil EngineeringJohns Hopkins UniversityBaltimoreUSA
  3. 3.Air Force Research Laboratory/RXWright-Patterson Air Force BaseDaytonUSA

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