Lie groups and the compatibility conditions for continua with rigid structure

摘要

A derivation of the compatibility conditions for a continuum with rigid structure undergoing finite deformations is proposed. The geometry of the Lie group of frame changes is used. The compatibility conditions are deduced by requiring the involutiveness of a distribution associated to the strain; their relationship with the Maurer-Cartan equations of the group of frame changes is demonstrated. Applications to micropolar and Cauchy continua are given.