Strain–damage coupled algorithm for cancellous bone mechano-regulation with spatial function influence

In this work, a bone adaptation law based on fully coupled stimulus function taking into account strain–damage effects and spatial function influence based on ruptured osteocytes processes concept have been developed and implemented into Abaqus code. Contrary to previous works where the spatial function was considered without damage influence, in the present model, we propose a novel idea to describe osteocytes ruptured processes using damaged spatial function. Also, the stimulus reference value for bone resorption threshold is considered cycles depending variable and an experimental fitted relation between the strain reference value and the cycle’s number was proposed. In order to reduce the computation time, the integration of the damage growth rate is based on the cycle blocks approach. The idea is that the real cycles number are reduced (divided) into equivalent cycles blocks. Damage accumulation is computed over the cycles blocks and extrapolated over the real correspond cycles. To illustrate the capabilities of the remodeling algorithm, four mechano-regulation laws have been implemented and tested corresponding to four stimuli functions: (i) strain based stimulus without damage influence, (ii) fully coupled strain–damage without spatial function influence, (iii) fully coupled strain–damage with non damaged spatial function influence and (iv) fully coupled strain–damage with damaged spatial function influence.