The plastic part of an elastic-plastic deformation is that remaining when the stress, and hence the elastic strain, is reduced to zero. Elastic deformation is that produced in this purely plastically deformed material by the action of stresses up to yield. The associated exact finite-deformation kinematics shows the almost universal assumption that the total rate of deformation is the sum of elastic and plastic rates to be in error. An incremental elastic-plastic theory is developed using the nonlinear kinematics. The theory is contrasted with that in common use and anomalies in the latter are discussed.

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