A mean field homogenization model for fiber reinforced composite materials in large deformation
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In the past years, advancements in manufacturing techniques have create composite materials with even complex micro-scale geometry. New meshing algorithm was developed to reduce the computational cost in simulating the yarn-yarn/matrix interaction [1]. To increase the numerical efficiency further, a micromechanically-based mean field homogenization (MFH) model for fiber reinforced composite materials is developed. The model idealizes the fiber and matrix interaction as a series of layered two-phase composite inclusions, in a similar fashion as [2], where the deformation compatibility and stress equilibrium constrains are carefully constructed to be adapted to fibrous material. The model is formulated in a large deformation framework with no restriction on the types of the fiber and matrix constitutive relations that can be used. The MFH model is implemented in UMAT and the homogenization results are compared to the direct numerical simulation (DNS) in ABAQUS/Standard. Several cases are tested to demonstrate the ability of the model to capture the hyperelastic/elasto-plastic stress-strain behaviour of the fibrous composites in different loading conditions. Figure 1 shows an example where the fiber reinforced composite material undergoes shearing in the fiber direction. The stress-strain relations obtained by the MFH is comparable with DNS model in large deformations with nonlinear fiber and matrix materials while the computational cost is significantly reduced.