This study presents a concurrent multiscale numerical framework for analyzing moisture-induced deformations in fiber network materials with specific applications to paper curl. The implementation extends the methodology introduced earlier by incorporating material inelasticity, which has been identified as crucial to predict accurately moisture-dependent mechanical behavior in fibrous materials. The framework operates on two scales simultaneously: at the microscale, fiber-to-fiber bonds are resolved using three-dimensional volumetric elements to capture complex strain fields induced by orthotropic hygroexpansion and inelastic phenomena (plasticity, viscoelasticity, and damage); at the macroscale, fibers are represented using Timoshenko beam elements with beam-to-beam contact. The scales are coupled through an energy-conserving transfer scheme where strains calculated at the joint level are mapped to the beam quadrature points while preserving the total strain energy between the scales. This approach allows for the explicit representation of thousands of fibers and joints in industrially relevant sheet sizes while accurately resolving the three-dimensional deformation at each bond. The implementation utilizes parallel computing to solve independent bond problems concurrently within Newton-Raphson iterations, ensuring numerical stability and convergence. Through parameterized simulations, we investigate how structural factors such as density variations, fiber orientation distribution, and material anisotropy contribute to paper curl. Numerical results demonstrate that the model successfully captures differential hygroexpansion through sheet thickness, revealing the relationship between microstructural parameters and macroscopic deformations. Including inelastic effects significantly improves prediction accuracy compared to purely elastic models, particularly under cyclic moisture conditions. This implementation offers a computationally tractable approach for analyzing moisture-induced dimensional instability in heterogeneous fibrous materials.