The vanishing of Riemann-Christoffel tensor is usually adopted as the compatibility condition of finite deformation. However, we prove in this paper by the method of Cesaro that this condition is necessary but not sufficient for guarantee of a single-valued, continuous displacement field. HISTORICAL SKETCH Solid mechanics developed in the outpouring of mathematical and physical studies following the great achievement of Isaac Newton (1642-1727) in stating the laws of motion, although it has earlier roots. The need to understand and control the fracture of solids seems to have been a first motivation.
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