“…The approach has been coupled with deformations in Coleman and Gurtin (1967) and Halphen and Nguyon (1975), with a subsequent rich literature, in the majority of cases related to plasticity and/or damage (see, e.g., Krajcinovic, 1996). The balance of microstructural actions can be reduced to the evolution equation that 42 Consequences of the covariance of the balance of energy of elastic simple bodies are discussed in Marsden and Hughes (1983), while for the covariance of the second law of thermodynamics, in the case of elastic-plastic materials, the first theorem published is in Mariano (2013). appears in internal variable schemes in the absence of external body actions (including even possible rotational microstructural inertia), microstress, and when the self-action is the sum of conservative and dissipative components (see Mariano, 2002 for details). However, the relation is just formal: the difference in the use of the notion of an observer continues to distinguish the two approaches.…”