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

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 func-tionally 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.

Automated summary

A hybrid analytical-numerical approach has been developed to determine the strain energy release rates (SERRs) in shear deformable functionally graded plates. The approach involves developing expressions for Mode I and Mode II SERRs, determining mode mixity using contour integral analysis, and using phase angle to numerically solve for a mode mixity parameter. The approach is then validated and used to investigate how SERRs and mode mixity vary across a wide range of stiffness gradations, crack lengths, and crack locations in a shear deformable functionally graded plate system.