Predicting the effective mechanical behavior of micro-architected structural elements has become a key challenge in engineering science. Many materials commonly used in stereolithography (e.g., epoxy resins and nylons) and laser powder bed fusion (e.g., some metallic alloys) exhibit different elastic responses in tension and compression. At the microscale, this asymmetry can be explained by the presence of microcracks or microvoids, inhomogeneous microstructures, and residual stresses induced by nonuniform solidification. These effects significantly influence the effective mechanical properties of manufactured metamaterials. Asymmetry in tension-compression can also arise on a macrolevel, if the geometry of the metamaterial’s sub-structure dictates the bi-modulus nature. In this work, a numerical implementation is proposed for a discrete-based constitutive material model that captures tension-compression asymmetry within a strain‑governed framework, whereby the elastic response depends on the sign of a specific combination of principal strains. Due to the tension-compression asymmetry, the problem becomes non-linear as material stiffness depends on the strain state. Two different approaches are discussed: one using physics-informed neural networks (PINNs) and the other using conventional non-linear finite element implementation. The main focus of this work is on PINNs, while the latter is used for verification. A multi-objective loss function is considered, in which the elastic energy for the proposed bi-modulus formulation is incorporated, and the kinematic boundary conditions are embedded directly into the neural network output using a distance function. The impact of tension-compression asymmetry is analyzed numerically on several benchmark problems, the pros and cons of the approaches are addressed.