An IGA-FEA model for flexoelectricity-induced healing of microcracks in cortical bone

The remodelling process in bones is closely related to electromechanical phenomena. In addition to streaming potentials and piezoelectricity, flexoelectricity has been found to serve as an initiator for remodelling in cortical bone. Since flexoelectricity is coupled to strain gradients, the effect is size-dependent and, accordingly, most relevant on small scales. This means that particularly microcracks which occur in the mechanically loaded bone under daily activity, are healed in response to flexoelectric initiation. More specifically speaking, flexoelectricity induces electric fields in the vicinity of such microcracks and thereby causes osteocyte apoptosis which is a pivotal event in the process of bone remodelling. Since experiments on such small scales are difficult to conduct, a numerical framework is established in this contribution which captures the flexoelectric initiation of bone remodelling as well as the remodelling process itself, including bone cell diffusion and progressive crack closure through surface growth. Due to the higher-order PDEs that result from the incorporation of flexoelectricity, a globally C1-continuous isogeometric analysis framework is adopted for the initiation process, whereas a classic finite element approach is proposed for the subsequent diffusion and growth processes. This framework is applied to a cortical bone sample with a narrow microcrack subject to mechanical loading. Growth is coupled to the activity of osteoblasts and incorporated numerically by a moving mesh algorithm. It is shown that the proposed framework can capture the entire process of cortical bone remodelling from its initiation until the successive healing of the microcrack.