Computational Methods for Debonding in Composites

310 H. Miled et al.
Fig. 15.13 Comparisons between isotropic and anisotropic fiber distribution on the first displacement
component
Incompressibility is defined by a Poisson ratio close to 0.5 which is equivalent
ton an infinite value for the Lame coefficient λ . The coefficient ξ is then taken as
following:
d.λ + 2µ
ξ = (15.41)
d
For isotropic incompressible case, Eq. 15.39 becomes:
�
∇. 2µε(u) − 2µ
d ∇.u1
�
− ∇q + fv = 0
(15.42)
∇.u = 0
The general case (Eq. 15.38), the problem is solved using the mixed finite
element method with the element P1+/P1 for (u,q).
The computed displacements were compared for isotropic and anisotropic oriented
fibers. Comparisons were done on the first displacement component, u1,
measured along the one-axis of the plate, at the symmetry plane. Figure 15.13 confirms
that fibers increase the plate rigidity in the flow direction: in the anisotropic
case, the displacement is lower than in the isotropic case.
15.5 Conclusion
In this work, an approach for prediction of the thermo-elastic properties of fiber reinforced
thermoplastics is presented. Fiber orientation is described by a second order
orientation tensor which is the solution of a tensorial convection-reaction equation.
Its resolution is carried out by a continuous approach based on the Galerkin Standard