The effective compliance of spatially evolving planar wing-cracks

We present an analytic closed form solution for anisotropic change in compliance due to the spatial evolution of planar wing-cracks in a material subjected to largely compressive loading. A fully three-dimensional anisotropic compliance tensor is defined and evaluated considering the wing-crack mechanism, using a mixed-approach based on kinematic and energetic arguments to derive the coefficients in incremental compliance. Material, kinematic and kinetic parametric influences on the increments in compliance are studied in order to understand their physical implications on material failure. Model verification is carried out through comparisons to experimental uniaxial compression results to showcase the predictive capabilities of the current study.