From an elastic point of view, the identification of equivalent homogenised models for heterogeneous structures is an active topic in computational homogenisation. For example, the masonry walls of blast or coking furnaces have different geometries, with blocks joined by mortar layers to enable stresses resulting from significant thermal gradients to be released. There are some well-established theoretical homogenisation results ([1,2]) for periodically repeating heterogeneous media, but computing the resulting effective properties requires solving a set of periodic auxiliary problems (AP-Per) on a representative volume element (RVE). The main challenge in numerical implementations lies in imposing displacement periodicity and adding constraints to eliminate rigid-body modes. In this talk, we will present a methodology that, under certain assumptions, is equivalent to the homogenisation results and avoids imposing explicit periodic displacement constraints. This methodology involves defining six basic displacement tests (D-BTs) on the RVE and specifying the relevant displacement vector components for each test ([3]), while the remaining boundary conditions are free. Assuming appropriate geometric symmetries in the RVE and orthotropic materials, we demonstrate that solving these six tests yields the same homogenised material as the AP-Per. Additionally, an associated algebraic system is obtained that relates the average stress and strain in the solutions of each of the six basic tests. Solving this system enables the effective properties of composite materials to be determined, with an implementation that is straightforward in standard Finite Element workflows, using either commercial packages or open-source codes. We will analyse the effectiveness and applicability of the proposed method to different periodic structures in engineering. The analysis will focus on the accuracy of approximating the displacement field and the associated von Mises stress.