On Micropolar Elastic Foundations

Abstract: 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.