TY - JOUR
T1 - On micropolar elastic foundations
AU - E.F. Athanasiadis, Adrianos
AU - Budzik, Michal Kazimierz
AU - Fernando, Dilum
AU - Dias, Marcelo Azevedo
PY - 2024/5
Y1 - 2024/5
N2 - The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar elasticity. Conversely, elastic foundation theory is widely employed in fracture mechanics and the analysis of delamination propagation in composite materials. This study aims to amalgamate these two frameworks, enhancing the elastic foundation theory to accommodate materials exhibiting micropolar behaviour. Specifically, we present a novel theory of elastic foundation for micropolar materials, employing stress potentials formulation and a unique normalisation approach. Closed-form solutions are derived for stress and couple stress reactions inherent in such materials, along with the associated restoring stiffness. The validity of the proposed theory is established through verification using the double cantilever beam configuration. Concluding our study, we elucidate the benefits and limitations of the developed theory by quantifying the derived parameters for materials known to exhibit micropolar behaviour. This integration of micropolar elasticity into the elastic foundation theory not only enhances our understanding of material responses but also provides a versatile framework for the analysis of heterogeneous materials in various engineering applications.
AB - The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar elasticity. Conversely, elastic foundation theory is widely employed in fracture mechanics and the analysis of delamination propagation in composite materials. This study aims to amalgamate these two frameworks, enhancing the elastic foundation theory to accommodate materials exhibiting micropolar behaviour. Specifically, we present a novel theory of elastic foundation for micropolar materials, employing stress potentials formulation and a unique normalisation approach. Closed-form solutions are derived for stress and couple stress reactions inherent in such materials, along with the associated restoring stiffness. The validity of the proposed theory is established through verification using the double cantilever beam configuration. Concluding our study, we elucidate the benefits and limitations of the developed theory by quantifying the derived parameters for materials known to exhibit micropolar behaviour. This integration of micropolar elasticity into the elastic foundation theory not only enhances our understanding of material responses but also provides a versatile framework for the analysis of heterogeneous materials in various engineering applications.
KW - Architected materials
KW - Elastic foundation
KW - Heterogeneous materials
KW - Homogenisation
KW - Mechanical metamaterials
KW - Micropolar elasticity
UR - http://www.scopus.com/inward/record.url?scp=85185845820&partnerID=8YFLogxK
U2 - 10.1016/j.euromechsol.2024.105277
DO - 10.1016/j.euromechsol.2024.105277
M3 - Journal article
SN - 0997-7538
VL - 105
JO - European Journal of Mechanics A - Solids
JF - European Journal of Mechanics A - Solids
M1 - 105277
ER -