Application of Non-Classical Micropolar Elasticity for Modelling and Analysis of Porous GBR Mesh Structures

Guided Bone Regeneration (GBR) meshes are used in dentistry as mechanical barriers to isolate and protect the area of bone loss from the surrounding tissue while allowing new bone growth. The design of porous GBR meshes can be a compromise between stiffness and porosity to meet mechanical requirements while facilitating the diffusion of nutrients for cell growth. Appropriate modelling can optimise the functionality of GBR meshes by designing microstructural parameters such as density, geometry, and spatial distribution of porosity. However, direct modelling and discretisation of such cellular materials can lead to cumbersome computations. This calls for equivalent constitutive laws that can consider microscopic features while ensuring computational efficiency. Since classical continuum theory cannot take into account the internal length scale of materials, non-classical continuum theories, that simultaneously use field description at the coarse level and preserve memory of the internal structure at a fine level, can circumvent this limitation. In the present work, the micropolar continuum is adopted to homogenise the heterogeneous porous model of GBR meshes. The mechanical parameters of the continuum are derived based on the strain energy equivalence of a porous plate with its correspondent micropolar model under prescribed loading. The effects of various architectural features, such as pore shapes, patterns, and sizes of the material parameters are investigated. The developed mechanical model can provide a useful framework for GBR mesh design, taking into account both mechanical and biomedical requirements. As an example, we have investigated different materials and arrangements to find micropolar constitutive parameters that are comparable to bone parameters reported in the literature. This allows the GBR mesh to possess the mechanical performance that matches the adjacent bones.