# Displacements representations for the problems with spherical and circular material surfaces with surface tension

## TL;DR

This paper develops modified displacement representations to analytically study spherical and circular material surfaces with surface tension, deriving explicit formulas for elastic fields and effective properties in composites.

## Contribution

It introduces modified displacement representations enabling analytical solutions for problems involving surface tension on spherical and circular interfaces.

## Key findings

- Derived closed-form expressions for local elastic fields.
- Calculated effective moduli of composites with surface tension.
- Extended models to include Gurtin-Murdoch and Steigmann-Ogden interface theories.

## Abstract

The displacements representations of the type used by Christensen and Lo (1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations are used to derive closed-form expressions for the local elastic fields and effective moduli of a macroscopically isotropic composite materials containing spherical and circular inhomogeneities with the interfaces described by the complete Gurtin-Murdoch and Steigmann-Ogden models.