Many common materials exhibit different elastic behaviour in tension and compression [1]. A key challenge in modelling such behaviour lies in formulating a consistent bi-modulus continuum theory, in particular, in identifying the quantity that governs the transition between tensile and compressive regimes and, consequently, determines the corresponding elastic moduli responsible for the material duality. For isotropic materials, the most widely known approach is the theory proposed by Ambartsumyan [2], who phenomenologically assumed that the transition is controlled by the signs of the principal stresses. Some recent works use, e.g, a deviatoric-volumetric split assumption of the strain energy function [1] and a granular micromechanics approach [3]. In this contribution, we propose a discrete-based constitutive material model that captures tension-compression asymmetry within a strain‑driven framework, whereby the elastic response depends on the sign of a specific combination of principal strains. We consider a series of benchmark problems, namely a pure shear load, volumetric load, and uniaxial load cases, and discuss (1) the decomposition of elastic strain energy, (2) the principal directions of the stress and strain tensors, and (3) the concept of classical Young's modulus and Poisson's ratio applied in the framework of bi-modulus materials. References [1] Latorre M., Montáns F. J., Bi-modulus materials consistent with a stored energy function: Theory and numerical implementation, Computers and Structures, 229, 106176, 2020. [2] Ambartsumyan S. A., Elasticity theory of different moduli, Trans. RF Wu and YZ Zhang. China Railway, Beijing, 1986. [3] Misra A., Placidi L., Emergence of bimodulus (tension-compression asymmetric) behavior modeled in granular micromechanics framework, Mathematics and Mechanics of Solids, 30, 1711-1726, 2025.