TY - GEN A1 - Malik, Alexander A1 - Hütter, Geralf A1 - Abendroth, Martin A1 - Kiefer, Bjoern T1 - Micromorphic FE2 simulation of plastic deformations of foam structures T2 - International Journal of Mechanical Sciences N2 - Capturing and predicting the effective mechanical properties of highly porous cellular media still represents a significant challenge for the research community, due to their complex structural interdependencies and known size effects. Micromorphic theories are often applied in this context to model the inelastic deformation behavior of foam-like structures, in particular to incorporate such size effect into the investigation of structure–property correlations. This raises the problems of formulating appropriate constitutive relations for the numerous non-classical stress measures and determining the corresponding material parameters, which are usually difficult to assess experimentally. The present contribution therefore alternatively employs a hierarchical micromorphic multi-scale approach within the direct FE2 framework to simulate the complex irreversible behavior of foam-like porous solids. The predictions of Cosserat (micropolar) and a fully-micromorphic theory are compared with conventional FE2 results and direct numerical simulations (DNS) for complex loading scenarios with elastic, elastic–plastic, and creep deformations. Therein, non-classical deformation modes of the microstructure resulting from the introduced micromorphic kinematics are visualized, as are the macroscopic hyperstresses and deformations. KW - Multi-scale KW - Homogenization KW - Size effects KW - Generalized continuum KW - Micromorphic theory KW - FE Y1 - 2024 U6 - https://doi.org/10.1016/j.ijmecsci.2024.109551 SN - 0020-7403 VL - 282 ER - TY - GEN A1 - Hütter, Geralf T1 - Interpretation of micromorphic constitutive relations for porous materials at the microscale via harmonic decomposition T2 - Journal of the Mechanics and Physics of Solids N2 - Micromorphic theories became an established tool to model size effects in materials like dispersion, localization phenomena or (apparently) size dependent properties. However, the formulation of adequate constitutive relations with its large number of constitutive relations and respective parameters hinders the usage of the full micromorphic theory, which has 18 constitutive parameters already in the isotropic linear elastic case. Although it is clear that these parameters are related to predicted size effects, the individual meaning of single parameters has been rather unclear. The present work tries to elucidate the interpretation of the constitutive relations and their parameters. For this purpose, a harmonic decomposition is applied to the governing equations of micromorphic theory. The harmonic modes are interpreted at the microscale using a homogenization method for a simple volume element with spherical pore. The resulting boundary-value problem at the microscale is solved analytically for the linear-elastic case using spherical harmonics resulting in closed-form expressions for all of the elastic 18 parameters. These values are used to predict the size effect in torsion of slender foam specimens. The predictions are compared with respective experimental results from literature. KW - Micromorphic theory KW - Homogenization KW - Size effect in torsion KW - Harmonic decomposition KW - Foam material Y1 - 2023 U6 - https://doi.org/10.1016/j.jmps.2022.105135 VL - 171 SP - 1 EP - 24 ER -