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The present work is a numerical prediction based initially on a reliable model validated by experiments under the same conditions used as ours with new concepts in Bi-composite plates. A system formulation approach of the adhesive in ductile and nonlinear damage behavior is used in this analysis This ductility is developed by the CZM technique implemented using the MATLAB program in ABAQUS computer code. For a numerical prediction of the ductile behavior of the adhesive, the CZM model is an extension of the pure modes (I and II) previously characterized in block by tests. This extension is trapezoidal in increasing stresses of the adhesive in its behavior law. The single lap joint configuration allows us to stress the glue joint to mixed-mode loading. The resistance of the assembled structures remains conditioned by the behavior of the adhesive until it is damaged and the rigidity of the attached plates. Therefore, our objective in this work is to cause the plasticization damage of the adhesive at different responses and levels. For this, the bi-composite graduation in concept and in graduation index largely plays the role of evaluation parameters. In order to test the adequacy for a good resistance, three different concepts of graduation in Bi-composite were proposed such as: concept1-concept1, concept2-concept2, and simple concept-simple concept. By these two cases of assemblies, these concepts have the advantage of having different assembly possibilities, The proposed concepts of graduated bi-composite plates showed an overcapacity of resistance on the assembly. The latter becomes important in the adequacy of concept of these assembled plates. Similarly, the results show that different responses and levels cause the damage by effect of these concepts. [ABSTRACT FROM AUTHOR]