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A thermodynamically consistent approach to microplane theory. II: Dissipation and inelastic constitutive modeling. (English) Zbl 0999.74013

The concept of thermodynamically consistent approach to microplane theory introduced in part I [see the foregoing entry] is dealt with more deeply in order to apply this approach to any kind of rheological behavior. To this aim, the microscopic strain components of one (micro)plane are derived by projection of the macroscopic strain tensor, leading to a kinematically constrained model. Then, according to the basic concept of microplane theory, the macroscopic material description is obtained by integrating the microplane stress-strain relations over all orientations of the microplane at a material point. The identification is made through the use of the principle of virtual power. The microplane laws are chosen such that the macroscopic version of Clausius-Duhem inequality is satisfied. This generic concept is applied to classical models of elasticity, elastic damage and elasto-plasticity. Finally, the results are documented by the analysis of pointwise texture evolution for the model problems provided by uniaxial tension and simple shear.
Reviewer: G.A.Maugin (Paris)

MSC:

74A60 Micromechanical theories
74A15 Thermodynamics in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74A20 Theory of constitutive functions in solid mechanics
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