The mechanical behavior of a heterogeneous material is strongly influenced by the response of its constituents (and their respective interactions) at lower scales. This fact accounts for the nonlinearities observed at the macroscale, and consequently, the challenges in formulating constitutive models capable of providing accurate predictions in a practical application context. Essentially, there are two primary ways to represent a heterogeneous material, either through Phenomenological Models at a Single Scale or through Multiscale Models. Multiscale models represent the most robust approach to depicting a heterogeneous material. In these models, the connection between macro and meso levels is typically made through the concept of a Representative Volume Element (RVE). The RVE is the smallest sample of the material that can statistically represent the mechanical behavior of the material. Typically, in multiscale model applications, it is assumed that an RVE exists and that its size is initially prescribed. However, the appropriate determination of an RVE for quasi-brittle materials remains a subject of study. This paper discusses the determination of RVEs for concrete using normalized graded aggregate curves. For this purpose, numerical simulations were performed using the Finite Element Method, employing constitutive models based on Phase Field theory. Throughout the study, issues related to the size of the RVE and the determination of ergodic properties are discussed. The influence of the aggregate gradation curve on the mechanical behavior of the RVE and the influence of the aggregate-mortar interface are also examined. Finally, the difficulties encountered in determining the RVE in a practical application context are presented.
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