In recent years, architected materials and structures have gained significant popularity due to their ability to reach enhanced performance for use in multifunctional and multidisciplinary applications. Among numerous options investigated, architected structures based on Triply Periodic Minimal Surfaces (TPMS) have gained increasing attention because they exhibit exceptional properties in multiple disciplines simultaneously. However, because of the complexities involved in the geometry representation and mechanical response of these structures, physics-based modeling for this problem class engenders a set of challenges. Recently, an IGA-based approach using general-purpose Kirchhoff—Love shells was proposed for TPMS-based structures [1]. The work included developing a pipeline to generate IGA-suitable models and carrying out large-deformation inelastic crushing simulations with self-contact to assess the ability of these structures to dissipate energy in extreme loading scenarios. In this talk, further advances in IGA-based architected materials and structures are presented, including looking at different surface architectures, considering strain-rate effects in the modeling, and a coupled formulation involving the coupling of stress and diffusion of voids/defects.