DRAFT Computational modelling of mechanically regulated bone adaptation Lukasz Kaczmarczyk ∗ and Chris J. Pearce cor Department of Civil Engineering, University of Glasgow, Rankine Building Abstract This paper presents a formulation and realisation of three-dimensional numerical sim- ulation of mechanically regulated bone adaptation. Attention is focussed on problem dis- cretization and solution algorithm tailored for shared memory multi-core computers. Pre- sented solution strategy is based on the hybrid finite element formulation where displace- ment, stress and density field are independently approximated. The model is restricted to small strains and does not involve gradients of the density field, however a generalisation is possible. Although presented method is applied for problem of bone remodelling, this formalism can be applied more generally to any multi-field problem of continuum mechan- ics, e.g. the classical chemo-thermo-elasticity or problems arising in inelasticity such as damage or plasticity, can be treated in an analogous way. Key words: bone remodelling, mechanical regulation, proxima femur, hybrid stress finite element, hpc computing 1 Introduction Biological tissues are unique in their ability to continuously adapt in response to their environment. Bone undergoes a continuous process of resorption and forma- tion throughout its lifespan called bone remodelling. This process occurs in re- sponse to mechanical stimuli and the microstructure evolves to provide an internal architecture that is optimised with respect to strength, stiffness and weight. The finite element based numerical simulation of bone and its functional adaptation to its mechanical environment has been undertaken for a number of years [1–4]. ∗ Corresponding author. Email addresses: lukasz@civil.gla.ac.uk (Lukasz Kaczmarczyk), pearce@civil.gla.ac.uk (Chris J. Pearce). Preprint submitted to Elsevier 27 January 2010