Nonlinear buckling of a spherical shell embedded in an elastic medium with imperfect interface

This work analyzes nonlinear buckling of a single spherical shell imperfectly bonded to an infinite elastic matrix under a compressive remote load. The inclusion is modeled using a nonlinear shell formulation and the matrix is treated as a linear elastic body. Imperfect bonding conditions are realized through a linear spring interface model. A variational method is used to derive the governing differential equations, which are cast into a tractable set of nonlinear algebraic equations using the Galerkin method. An incremental iterative technique based on the modified Newton–Raphson method is employed to find the critical load of the system. The accuracy and convergence properties of the proposed method are validated through finite element analysis. The study is relevant to the analysis of compressive failure of syntactic foams used in marine and aerospace applications. Results are specialized to glass particle-vinyl ester matrix syntactic foams to test the hypothesis as to whether microballoons’ buckling is a dominant failure mechanism in such composites under compression. Parametric studies are conducted to understand the effect of interfacial properties and inclusion wall thickness on the overall mechanical behavior of the composite. Comparisons between analytical findings and experimental results on compressive response of syntactic foams and isolated microballoons indicate that inclusion buckling is unlikely a determinant of compressive failure in vinyl ester-glass systems. In particular, the matrix is found to exert a beneficial stabilizing effect on the inclusions, which fail under brittle fracture before the onset of buckling.