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A thermodynamically consistent approach to microplane theory. I: Free energy and consistent microplane stresses. (English) Zbl 0999.74012
The first in a series [for part II, see the following entry], this paper presents a thermodynamical framework for the construction of consistent microplane stresses and their corresponding integral relation to the macroscopic stress tensor. It is reminded that microplane models are based on the assumption that the constitutive equations of the material may be established between normal and shear components of stress and strain on planes of generic orientation (so-called microplanes), rather than between tensor components or their invariants. The stress tensor then is obtained by integrating stresses on microplanes of all orientations at a point. Here a free-energy potential is defined at the microplane level. However, it seems that many existing formulations of microplane models do not fully obey this thermodynamical scheme. As a consequence, a lack of work conjugacy (in the principle of virtual work) may be exhibited between some of the microplane stress and strain variables, and spurious energy dissipation or generation may exist under certain load cycles for some of the models.
Reviewer: G.A.Maugin (Paris)

MSC:
74A60 Micromechanical theories
74A15 Thermodynamics in solid mechanics
74A20 Theory of constitutive functions in solid mechanics
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