Numerical Analysis of Solid and Shell Models of Human Pelvic Bone
by
John Antoni
Silesian University of Technology, Department for Strength of Material and Computational Mechanics, Konarskiego 18A, 44-100 Gliwice, POLAND

Pelvic bone is an important supporting element in locomotion system of human. It is very difficult or impossible to measure the strain and stress ïn vivo" because the safety of patient should be taken into account. There are only two possibilities: model testing and numerical calculations. Complex geometry and material structure of bone tissue as well as its state of load or physiological reactions complexity, cause huge variety of acceptable assumption in 3D numerical models and shell models which exerts an influence on the calculation outcomes. Numerical modeling of human pelvic bone makes possibilities to determine the stress and strain distribution in bone tissue. Some simplifications in numerical model are performed. During numerical analysis it can be observed that stress distribution in numerical model of human pelvic bone depend on boundary conditions and yield criteria. The values of maximal reduced stresses are changed and the regions too. The present work defines stress and strain distribution in human pelvic bone using earlier studies made in Department for Strength of Material and Computational Mechanics in Silesian University of Technology, adding new elements in numerical model's structure and load caused by muscle tensions. 3D numerical model of pelvic bone have been worked out relying upon programs PATRAN, PATRAN/FEA. Eight-nodes solid elements illustrating 3D stress distribution were used for modelling.. Separate solid elements layers are modelled by cortical and trabecular bone. At present homogeneous elastic properties within a certain group of tissue as well as continuum are assumed. Cortical bone is modelled by one layer of elements while trabecular bone one or more, depending on model's bone tissue's thickness. On the basis of data from assumed Young's modulus 15GPa and 100MPa for cortical and trabecular bone respectively. In shell model assumed Young's modulus 10GPa, Poisson's ratio 0.3, and quotient of compression strength to tensile strength 1.5. Stress and strain distribution of human pelvic bone is a result of external load coming from upper body part's weight and muscles forces. Referring to earlier works, the model takes up 23 muscle tensions influencing through pelvic bone and tendons on insertions' surfaces. Numerical results are obtained for many cases of boundary conditions. The stiffness of axial elements are changed. There is only one load case - maximal load. The results hardly depend on boundary conditions. Here, in acetabulum boundary conditions are given using 20 axial elements (in radial co-ordinate). In contact area with sacral bone boundary conditions are given using axial elements in two co-ordinates, respectively. In pubic symphysis boundary conditions are given in symmetry plane as restraints in selected co-ordinates (selected components in nodes). Analysis of results is performed using three yield criteria: maximum shear-stress (Tresca) criterion, shear-strain energy (von Mises) criterion and Burzynski's criterion (modification of shear-strain energy criterion with respect to different value of compression strength and tensile strength). Presented numerical model of pelvic bone is performed using finite elements and assumed constraints, with a little approximation mapping anatomical shape of the bone and its character of joint in pubic symphysis, on the point of contact with sacral bone and thighbone's head in acetabulum of pelvic joint. Numerical analysis of human pelvic bone shows that stress distribution depend on boundary conditions, e.g. on stiffness of given restraints. The stress distribution and maximal value of reduced stresses depend on yield criteria. In selected model the difference increases over 50MPa, e.g. over 30%. When the Burzynski's criterion is applied the maximal value of reduced stresses decrees. It seems that Burzynski's criterion is closer to real existing conditions.

Date received: January 31, 2000