A New Constitutive Relation for Homogeneous Isotropic Materials by FEM Model of the Brazilian Splitting Test

The paper studies the behavior of homogeneous isotropic materials by performing appropriate numerical analyses and utilizing suitable FEMs to reproduce the Brazilian splitting test. Starting with a theoretical approach and adopting suitable numerical simulations, a new formula that is able to characterize the Young’s modulus is presented. To this end, in addition to the analysis of the specimen’s response in terms of stresses and strains, the real displacement field resulting from the real kinematical constraints on the specimen is determined. Therefore, the Brazilian test is taken as a reference test and the specimen’s behavior is derived by taking advantage of both the theoretical approach and numerical simulations developed in the ANSYS 2021 R1 environment. The latter allows us to define a new mathematical relation representing the missing part of the kinematical field. Furthermore, a new formula which explicitly relates the Young’s modulus of the material to the geometrical characteristics of the specimen, to the acting force, and to a measured selected displacement is proposed. Future developments will include adopting the proposed formulas for the identification of other mechanical parameters of the material, e.g., by adopting a full-field contactless approach to displacement measurement and studying the behavior of specimens with different geometrical characteristics.