Effective elastic moduli and failure mechanisms of a random assembly of thin walled glass microbubbles

In this work a methodology is presented to estimate the elastic properties and failure mechanisms of an assembly of random, brittle microbubbles. The approach is based on the mechanics of frictionless micro-contact between hollow spherical shells by employing relations from classical shell theory and verified by two dimensional axisymmetric Finite Elements. The estimated values are in agreement with available experimental values. Moreover, a granular type analytical homogenization model provides an isotropic elastic constitutive law to be used for the macroscopic deformation of an assembly of glass micro-bubbles when it is compressed by external loads. In addition, approximate estimates are also proposed for two important micro-failure mechanisms of such assemblies that relate either to the splitting or to the buckling of a brittle spherical shell, prior its complete crushing. The results are novel and are expected to enhance the application of glass microbubbles directly in acute thermal insulation problems such as liquid hydrogen storage.