Upscaling from a micro-mechanics model to capture laminate compressive strength due to kink banding instability

Analyzing failure mechanics of fiber-reinforced media that correspond to different length scales with the goal of up-scaling is addressed in this paper with respect to compressive kinking instability in fiber reinforced laminae. Using the concentric cylinder model (CCM) as a representative element of a lamina, J2 deformation theory along with Hill’s anisotropic plasticity theory is used to extend the constitutive model for the fiber-matrix cylinder, and hence the lamina, into the nonlinear regime. The model requires the elastic properties of fiber and matrix, the fiber volume fraction and the nonlinear shear response of the polymer matrix. An 8-layer laminate is up-scaled using this method by homogenizing the off-axis laminae and retaining micro-mechanics in the 0° laminae, and results are compared against a discrete fiber-matrix micro-mechanical model of the laminate. The effect of homogenizing the laminae on the compressive response of the laminate is investigated.