, Volume 56, Issue 2, pp 95-105

On Compatibility Conditions for the Left Cauchy–Green Deformation Field in Three Dimensions

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A fairly general sufficient condition for compatibility of the left Cauchy–Green deformation field in three dimensions has been derived. A related necessary condition is also indicated. The kinematical problem is phrased as a suitable problem in Riemannian geometry, whence the method of solution emerges naturally. The main result of the paper is general in scope and provides conditions for the existence of solutions to certain types of overdetermined systems of first-order, quasilinear partial differential equations with algebraic constraints.