A hybrid analytical–numerical approach for the determination of strain energy release rates in shear deformable functionally graded plates

Abstract

A hybrid analytical–numerical approach is developed for the determination of strain energy release rates (SERRs) in shear deformable functionally graded plates. A two-plate system is considered, where the plates are functionally graded in the thickness direction and a crack exists between the two plates. Expressions for Mode I and Mode II SERRs are developed in terms of applied loads and moments on the two-plate system along with accompanying compliance coefficients. Mode mixity is then determined with the aid of contour integral analysis, where phase angle is used to numerically solve for a mode mixity parameter. Upon validation, the approach is used to characterize how SERRs and mode mixity vary over a comprehensive range of stiffness gradations, crack lengths, and crack locations for a shear deformable functionally graded plate system.