Issue 33

M.A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 33 (2015) 357-367; DOI: 10.3221/IGF-ESIS.33.39 365 Figure 5 : Yield, bounding, and failure surfaces in the s 1 -s 2 deviatoric space for the two-surface model. In summary, the two-surface model and its variations combine elements of both Mróz and NLK multi-surface models, as compared in Tab. 2. Similarly to Mróz multi-surface models, it is an “uncoupled formulation” since the generalized plastic modulus P is not a function of the translation directions, only of the distance | | i v   . On the other hand, similarly to NLK multi-surface models, the yield and all hardening surfaces translate, the surface translation direction can (and should) use a non-linear equation, and the generalized plastic modulus P continuously varies instead of being assigned piecewise- constant values. Mróz multi-surface two-surface NLK multi-surface Number M of yield and hardening surfaces: M  2 M  2 M  1 Surface translation during plastic straining: no translation outside active surface the yield and all hardening surfaces (including the bounding surface) translate Surface translation direction i v   : defined by linear rules such as Mróz Mróz for 1 d    ; linear or non-linear rule for 1 2 d d        defined by non-linear rules Surface backstress variation 1 d    during plastic straining: 1 d    from the active surface i  i A is the only 0 i d     all surface backstress increments 1 d    (for i  1, 2, …, M ) are different than zero Generalized plastic modulus P : piecewise-constant P  P i from the active surface i  i A non-linear and continuously varying, calculated from relative positions among the yield and all hardening surfaces Consistency condition that prevents s   from moving outside any surface: used to calculate the backstress increments 1 d    and associated surface translations c i ds   used to calculate the non-linear P Table 2 : Comparison among the Mróz multi-surface, two-surface, and NLK multi-surface model formulations, to predict multiaxial kinematic hardening effects.