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Second‐order and affine estimates for the behavior of viscous polycrystals
Author(s) -
M. Bornert,
R. Masson,
Castañeda P. Ponte
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.20000801305
Subject(s) - viscoplasticity , thermoelastic damping , tangent , creep , nonlinear system , linearization , isotropy , homogenization (climate) , affine transformation , slip (aerodynamics) , mathematics , materials science , mathematical analysis , mechanics , geometry , physics , thermodynamics , constitutive equation , composite material , thermal , biodiversity , ecology , quantum mechanics , finite element method , biology
The recently proposed second‐order and affine estimates for the effective behavior of nonlinear heterogeneous materials rely on the same linearization procedure and refer to some “thermoelastic comparison composite”. But both approaches differ in the way the overall nonlinear answer is defined, either through average stress‐strain relations or energy considerations. When combined with the linear self‐consistent model, they provide new tools for the predictions of the behavior of viscoplastic polycrystals (steady state creep). They are compared to each other and to other more classical estimates (incremental and tangent) in the following situations.: a 2D antiplane model problem for which efficient rigorous upper bounds are available, the creep of isotropic aggregates of FCC crystals and HCP crystals with different critical stresses on the basal and prismatic slip systems.