On the Application of Non-Linear Rheological Models In Longitudinal Fracture Analysis of Beams Made of Functionally Graded Materials

This theoretical paper is devoted to a non-linear rheological model and its application in fracture analysis of a beam structure with an arbitrary number of longitudinal vertical cracks. The beam under consideration is a functionally graded material with viscoplastic behavior. The rheological model is structured by springs, dashpots, and a frictional slider that considers the plastic strains in the beam. The model is with two consecutive units. Solutions for the time-dependent strain energy release rate for each crack in the functionally graded beam structure under external mechanical loading are obtained using the rheological model. The J-integral is applied to control the solutions obtained. The solutions consider the viscoplastic behavior and the progressive variation of functionally graded material properties in the beam structure. It is shown that the solution derived in the present paper can be applied to examine the relation between the distribution of mechanical properties and the longitudinal fracture in functionally graded structural materials with viscoplastic behavior.