SOME AXIOMS AND THEOREMS IN DAMAGE MECHANICS AND FATIGUE OF MATERIALS

The treatments of problems in continuum damage mechanics (CDM) that ap pear in the scientific literature are based on a number of more or les s explicit assumptions. In this paper, these assumptions are reformula ted and shown to form a single axiomatic framework of both the ''inter nal variables'' and the ''multifield continuum'' schemes: the fundamen tal features of both descriptions are thus recognized and correlated w ith the general principles of mechanics. These developments are based on the general theory of actions developed by Coleman and Owen (Colema n, B. D. and Owen, D. R. (1974). A mathematical foundation for thermod ynamics. Archives of Rational Mechanical Analysis 54, 1-104; (1975). O n thermodynamics and elastic plastic materials. Archives of Rational M echanical Analysis 59, 25-51; (1977). On thermodynamics of semi-system s with restrictions on the accessibility of states. Archives of Ration al Mechanical Analysis 66, 173-181), which is presented in Section 2 i n a way slightly different from usual. Then, five axioms for CDM are i ntroduced in Section 3, and related theorems and corollaries are prove d. Finally, the Palmgren-Miner's rule of fatigue damage and its limita tions are reformulated in the context of the established general frame work. (C) 1997 Elsevier Science Ltd.