The paper presents an extension of the complementary work bounding principle of Hodge (1966) for integration along the path of loading for a statically loaded elastic-plastic body. Using an internal variable framework, the concept of a piecewise holonomic constitutive equation, updated at discrete intervals along the loading path, is introduced. It is shown that the complementary work over the entire path decreases (or does not increase) each time the last interval is subdivided. The result has some interesting implications with regard to the formulation of a mechanical principle for time discretisation along the loading path, and these are explored.

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