Material G-structures – a bridge

between Differential Geometry and Continuum Mechanics.

Abstract: As is well known a uniform elastic body is rich in geometric structure, a fact that has been successfully exploited to model continuous distributions of dislocations and other defects, thermal stresses, and residual stresses in general.

The basic geometric object involved is a G-structure which reflects the mechanical properties of the material. In this lecture we shall review the theory for simple uniform materials, but also their extensions to Cosserat media and functionally graded materials.