It is presented a rigorous framework developed for formulation of constitutive models. Based on representation theory for tensor functions and scale-bridging theorems, this framework enables the development of constitutive models that account for the influence of crystallographic structures and deformation mechanisms on the macroscopic behavior.
First, a new three-dimensional analytical criterion for description of the onset of plastic deformation in cubic single crystals is presented. The criterion is pressure-insensitive and form-invariant to any transformation belonging to the symmetry class of the given crystal. For most FCC single crystals the criterion involves five independent coefficients, which can be determined based on the yield stresses in different crystal orientations. Comparisons with single crystal data on aluminum and copper single crystals and applications to forming of single crystals are presented.
Next, it is shown that using this new criterion for the description of the plastic behavior of the constituent grains, for ideal texture components, the yield stress and plastic strain ratios can be obtained analytically. For the case of strongly textured sheets, the effect of individual texture components on the anisotropy in plastic properties of the polycrystalline sheets is predicted with improved accuracy ().
Illustration of the generalized invariants based-approach to modeling both anisotropy and tension-compression asymmetry in yielding and plastic flow is next discussed. Applications of the developed plastic potential to the simulation of the quasi-static and dynamic response of HCP-titanium and zirconium are discussed.
Finally, main contributions towards elucidating the role of the plastic deformation on damage evolution are briefly presented. Special attention is given to addressing the open problems posed in the mechanics community in the late 1960’s concerning the manner in which the matrix plastic behavior influences damage evolution (see ).
 O. Cazacu, B. Revil-Baudard, N. Chandola  A yield criterion for cubic single crystals, International Journal of Solids and Structures, 151, 9-19.
 O. Cazacu O, B. Revil-Baudard, N. Chandola, Plasticity-Damage Couplings:From Single Crystal to Polycrystalline Materials, Springer, ISBN 978-3-319-92921-7.