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.
TERESI L, & TIERO A (1997). Lie Groups and the Compatibility Conditions for Continua with Rigid Structure. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 35(12/13), 1195-1202 [10.1016/S0020-7225(97)00105-5].