Improved Extended Finite Element Method And Its Application On Porous Bio-ceramic

Scaffold design plays an important role in the bone tissue repair engineering. Porous bio-ceramic is composed by porosities and hydroxyapatite skeleton. After implanted in the human body, imporper use or secondary trauma would cause the implants fracture and failure. On one hand, the porosity redistributed the stress field of the implant and decreased its carrying capacity. On the other hand, micro-cracks are inevitable during the preparing and using course. Under the influence of porous, the stress concentration near the micro-crack tip is likely to be increased, and the crack would be propagated unstably. Therefore, it is important to study the mechanical property on cracked porous bio-ceramic.In this paper, based on the improved extended finite element method(XFEM), problems of cracked porous bio-ceramic are studied:(1) the formulas of XFEM are derived. A user element subroutine(UEL) based on the platform of ABAQUS is coded, and used to solve discontinuous problems such as cracks and holes. By the research on fracture parameters, it is found that the accuracy of stress intensity factor(SIF) calculated by displacement extrapolation is lower, but expanded the range of crack tip enrichment appropriately could improve the accuracy. And it is also found that the square enrichment is superior to the commonly used circular enrichment. The optimal enrichment sizes are given, while the errors analysis is presented. Based on the interaction intergral method, the codes are compiled to suitable for XFEM, and the integral paths are studied. Compared with the displacement extrapolation method, the interaction integral method has more advantages in the accuracy and results stability.(2) In the determination process of element types which affected by the crack tip and holes, identification mistake may occur by using tranditional level set method. Corrected level set method is developed and used to solve element type identification and element sub-division problems, which expand usable range of level set method.(3) The interaction between the cracks and pores of porous bio-ceramic model are studied. It is found that for circle hole, the center position and pore size affected the crack tip stress field greatly. In different arrangement, when the distance between the elliptical hole farther in vertical direction, the existence of holes amplified the crack tip stress field. When the distance between the elliptical hole decreases(θ=45°), the existence of holes have weak shield effect on the crack tip stress field, in this situation the structure is relatively stable. When the distance between the elliptical hole decreased(θ=30°), the existence of holes have great shield effect on the crack tip stress field. The small holes shielding effects are higher than the elliptical holes with increased axial ratio. In this situation, the existence of holes alleviated the crack tip singularity, to some extent, prevent the crack propagation. Meanwhile, the pores sizes satisfied the biological needs. This type of arrangement has certain significant to design the structure of porous bio-ceramic as a human implant.(4) Typical model are calculated by improved XFEM, the crack propagation paths are predicted. Meanwhile, the specimens are prepared and the experiment has been done. Digital image corration(DIC) method is used to obtain the deformation field, and the crack propagation paths are identified by digital image processing techniques. Comparison results show that the results by the improved XFEM are in accordance with the experimental results.(5) The porous bio-ceramics mechanical properties in the using process are studied. As an example of randomly distributed pores with different pore sizes and pore morphology, the deduction of the porous bio-ceramics were extracted as a simplified model, then the extracted model are used to do the simulation and the crack propagation paths were predicted.