Universitätsbibliothek
Weimar Open Access

This study is focused on finite element analysis of a model comprising femur into which a femoral component of a total hip replacement was implanted. The considered prosthesis is fabricated from a functionally graded material (FGM) comprising a layer of a titanium alloy bonded to a layer of hydroxyapatite. The elastic modulus of the FGM was adjusted in the radial, longitudinal, and longitudinal-radial directions by altering the volume fraction gradient exponent. Four cases were studied, involving two different methods of anchoring the prosthesis to the spongy bone and two cases of applied loading. The results revealed that the FG prostheses provoked more SED to the bone. The FG prostheses carried less stress, while more stress was induced to the bone and cement. Meanwhile, less shear interface stress was stimulated to the prosthesis-bone interface in the noncemented FG prostheses. The cement-bone interface carried more stress compared to the prosthesis-cement interface. Stair climbing induced more harmful effects to the implanted femur components compared to the normal walking by causing more stress. Therefore, stress shielding, developed stresses, and interface stresses in the THR components could be adjusted through the controlling stiffness of the FG prosthesis by managing volume fraction gradient exponent.

A Semi-Concurrent Multiscale Approach for Modeling Damage in Nanocomposites

A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed.

Meshfree methods (MMs) such as the element free Galerkin (EFG)method have gained popularity because of some advantages over other numerical methods such as the finite element method (FEM). A group of problems that have attracted a great deal of attention from the EFG method community includes the treatment of large deformations and dealing with strong discontinuities such as cracks. One efficient solution to model cracks is adding special enrichment functions to the standard shape functions such as extended FEM, within the FEM context, and the cracking particles method, based on EFG method. It is well known that explicit time integration in dynamic applications is conditionally stable. Furthermore, in enriched methods, the critical time step may tend to very small values leading to computationally expensive simulations. In this work, we study the stability of enriched MMs and propose two mass-lumping strategies. Then we show that the critical time step for enriched MMs based on lumped mass matrices is of the same order as the critical time step of MMs without enrichment. Moreover, we show that, in contrast to extended FEM, even with a consistent mass matrix, the critical time step does not vanish even when the crack directly crosses a node.

A computational library for multiscale modeling of material failure