Bone Tissue - Meshless Methods in Biomechanics - page 240

Fig. 6.9 Proposed bone remodelling algorithm

Then, it is possible to establish the nodal connectivity (the influence-cells), con-
struct the integration mesh and determine the interpolation functions. In this early
phase the essential and natural boundary conditions are enforced and the material
properties are allocated to the respective domain areas. Afterwards, the iterative
remodelling algorithm is initiated.
In the first step of the iterative loop a trial linear analysis of the problem is
performed in order to obtain the principal directions of the stress field. In this first
step no remodelling takes place, the only purpose of this first step is to align the
material constitutive matrix of each interest point with the principal direction of
the respective maximum principal stress obtained in each interest point. Therefore
in the first step of the iterative loop, i ¼ 0, it is considered an initial isotropic
constitutive elastic matrix, obtained from the compliance matrix presented in
Sect. 2.1.2 , the local stiffness matrix for each integration point is constructed and
afterwards assembled into a global stiffness matrix K i . Since the presented
remodelling algorithm permits to consider simultaneously several load cases, for
each load case j the correspondent displacement field is obtained with u i = K i f j
and subsequently the respective strain field e i and stress field r i can be deter-
mined. The principal stresses, r ð n Þ i , and directions, n i , are obtained using the