  In this work, a mathematical model based on interface energy is proposed
within the framework of surface continuum mechanics to study the dynamics of
encapsulated bubbles. The interface model naturally induces a residual stress
field into the bulk of the bubble, with possible expansion/shrinkage from a
stress-free configuration to a natural equilibrium configuration. The
significant influence of interface area strain and the coupled effect of
stretch and curvature is observed in the numerical simulations based on
constrained optimization. Due to the bending rigidity related to additional
terms, the dynamic interface tension can become negative, but not due to the
interface area strain. The coupled effect of interface strain and curvature
term observed is new and plays a dominant role in the dominant compression
behavior of encapsulated bubbles observed in the experiments. We validate our
model by fitting experimental data of $1.7\,\mu$m, $1.4\,\mu$m, and $1\,\mu$m
radii bubbles by calculating the optimized parameters. Our work also highlights
the role of interface parameters and natural configuration gas pressure in
estimating the size-independent viscoelastic material properties of
encapsulated bubbles with interesting future developments.
