Abstract
FGM (functionally graded materials) have experienced rapid expansion in recent years in several industrial fields. The analysis of their mechanical behavior by the finite element method requires the use of subroutines established under a FORTRAN compiler given the difficulty in implementing the type of behavior of the materials constituting the FGM. Our work aims to establish a program in MATLAB (UMM) making possible to introduce the behavior of the FGM by element in the mesh model of the structure, hence the advantage and reliability of graded the material in three dimensions for two or even three constituents of FGM and secondly, for different geometric designs. This technique is more sensitive to the mesh, hence the adaptation strategy of a driven mesh in order to improve the precision and the convergence of results under minimal computation time. The constitutive law of our model follows the von Mises equivalent stress flow theory with a hardening variable in incremental form. Moreover, to describe the elastic–plastic behavior of FGM, the model of TTO (Tamura-Tomota-Ozawa) was used for both methods that of UMAT in the form of a numerical algorithm and for our new method in the form of calculated values by the MATLAB code. The parameters used in the two calculation methods are taken from the results of stress–strain tests of the two materials; ceramic (TiB; Titanium mono biorde) and metal (Ti; Titanium). A comparison between the two methods has taken place in the form of load–displacement curves in order to present the capacities of our technique with respect to the usual UMAT technique. However, for damage, the use of the XFEM technique in our UMM method has shown its advantage in the separation of the structure after crack initiation. The crack path as well as its propagation speed under the effect of the volume fraction exponent of the FGM has been highlighted. The two models used in this study (UMM and UMAT) were validated on the one hand with analytics through the TTO model and on the other hand by the experimentation of a tensile test.
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