Continuum Mechanics and Thermodynamics

, Volume 30, Issue 3, pp 573–592 | Cite as

Mechanics of an elastic solid reinforced with bidirectional fiber in finite plane elastostatics: complete analysis

  • Mahdi Zeidi
  • Chun I. L. Kim
Original Article


A continuum-based model is presented for the mechanics of bidirectional composites subjected to finite plane deformations. This is framed in the development of a constitutive relation within which the constraint of material incompressibility is augmented. The elastic resistance of the fibers is accounted for directly via the computation of variational derivatives along the lengths of bidirectional fibers. The equilibrium equation and necessary boundary conditions are derived by virtue of the principles of virtual work statement. A rigorous derivation of the corresponding linear theory is developed and used to obtain a complete analytical solution for small deformations superposed on large. The proposed model can serve as an alternative 2D Cosserat theory of nonlinear elasticity.


Finite plane deformations Fiber-reinforced material Bidirectional fiber Superposed incremental deformations Strain-gradient theory 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of AlbertaEdmontonCanada

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