Generalized materials

Recently, metamaterials have attracted massive attention in industry and academia. These artificially produced objects have physical properties not present in naturally occurring materials and have applications in several fields, such as biomedicine and stealth technology. More than standard elasticity models are required to discretize these hand-made materials and complicated real-life materials such as bones. The arising models incorporate additional length scales and fields. Examples are Cosserat elasticity and the (relaxed) micromorphic continua. The extra parameters and fields lead to potential locking behaviour. We constructed and analyzed stable mixed methods for the relaxed micromorphic model [2021, 2022, 2024, 2025]. In Cosserat elasticity, the limit process when the coupling constant tends to infinity leads to the couple stress problem, commonly used to model generalized materials. We presented and analyzed parameter-robust mixed methods for linear Cosserat elasticity combining the mass-conserving mixed stress (MCS) and tangential-displacement and normal-normal stress continuous (TDNNS) methods [2024].