An Extension of Duhamel’s Analogy to Plasticity

It is shown that the Duhamel analogy of classical elasticity theory may be extended without modification to the incremental theory of plasticity, when the loading function is temperature independent. For a class of temperature-dependent loading functions the analogy of the Duhamel type is shown to hold: (a) When the temperature field is stationary; (b) for problems in which the elastic and plastic components of strain individually satisfy compatibility; or (c) when the material is rigid plastic, provided the medium is interpreted as nonhomogeneous. Examples of particular correspondences are discussed. It is also noted that for linear viscoelastic materials in which volume changes are purely thermoelastic the transformations in the analogy are identical to those for elasticity.