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The Yang-Mills minimal replacement and minimal coupling constructs for a semisimple Lie group are extended to the non-semisimple internal symmetry group of a medium with microstructure. The microstructure is modeled in the medium by a set of deformable vector fields. The internal symmetry associated with global transformations of the vector fields becomes local through the introduction of compensating gauge potentials (gauge connection) by minimal replacement. Covariant torsion and curvature quantities formed by derivatives of the gauge potentials correspond to defect densities and currents admitted by the vector fields. The local internal symmetry group is finally broken down to its subgroup SO(3) T(3) allowing thus for the existence of conservation laws of linear and angular momentum. 1989.
International Journal of Engineering Science
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