Acta Mechanica

, Volume 230, Issue 5, pp 1745–1780 | Cite as

A multiphase internal state variable model with rate equations for predicting elastothermoviscoplasticity and damage of fiber-reinforced polymer composites

  • Ge HeEmail author
  • Yucheng Liu
  • D. J. Bammann
  • D. K. Francis
  • M. Q. Chandler
  • M. F. Horstemeyer
Original Paper


This paper explores the integration of an internal state variable (ISV) model for polymers (Bouvard et al. in Acta Mech 213(1):77–96, 2010; Int J Plast 42:168–193, 2013) with damage evolution (Horstemeyer and Gokhale in Int J Solids Struct 36:5029–5055, 1999; Horstemeyer et al. in Theor Appl Fract Mech 33(1):31–47, 2000; Francis et al. in Int J Solids Struct 51:2765–2776, 2014) into a multiphase ISV framework (Rajagopal and Tao in Advances in mathematics for the applied sciences, World Scientific, Singapore, 1995; Bammann in Proceedings of 2nd international conference on quenching and the control of distortion, vols 4–7, 1996) that features a finite strain theoretical framework for fiber-reinforced polymer (FRP) composites under various stress states, temperatures, strain rates, and history dependencies. In addition to the inelastic ISVs for the polymer matrix and interphase, new ISVs associated with the interaction between phases are introduced. A scalar damage variable is employed to capture the damage history of the FRP, which comprises three damage modes: matrix cracking, fiber breakage, and deterioration of the fiber–matrix interface. The constitutive model developed herein employs standard postulates of continuum mechanics with the kinematics, thermodynamics, and kinetics being internally consistent, whose ISVs can be either calculated from molecular dynamics simulations or calibrated through microstructural characterizations for specific FRPs. The developed elastothermoviscoplasticity and damage modeling framework is then employed to model the internal damage evolution of a glass fiber-reinforced polyamide 66 (Rolland et al. in Compos Part B Eng 90:65–377, 2016) in terms of above three damage mechanisms. A detailed description of the model parameter identification process is given by using the example of a unidirectional glass fiber-reinforced epoxy, and the mechanical behaviors and properties of the composites at varying temperature and fiber volume fraction are predicted by the model, which are in good agreement with the experimental result.


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This work is sponsored by Mississippi NASA EPSCoR through its Research Infrastructure Development (RID) Program. The authors are grateful to Dr. Nathan Murray and other personnel in that program for their support. The authors are also grateful to the support provided by the Center for Advanced Vehicular Systems (CAVS) at Mississippi State University (MSU). Dr. M. Q. Chandler would also like to thank the Army ERDC for supporting her on this project.


The funding was provided by Mississippi Space Grant Consortium.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Ge He
    • 1
    • 2
    Email author
  • Yucheng Liu
    • 1
    • 2
  • D. J. Bammann
    • 1
    • 2
  • D. K. Francis
    • 1
    • 2
  • M. Q. Chandler
    • 3
  • M. F. Horstemeyer
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringMississippi State UniversityMississippi StateUSA
  2. 2.Center for Advanced Vehicular SystemsMississippi State UniversityMississippi StateUSA
  3. 3.Army Engineering Research and Development Center (ERDC)VicksburgUSA

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