Numerical Modelling of Crack Propagation in Cement PMMA: Comparison of Different Criteria

Abstract

Modelling of a crack propagating through a finite element mesh under mixed mode conditions is of prime importance in fracture mechanics. In this paper, three different crack growth criteria and the respective crack paths prediction in the cement mantle of the reconstructed acetabulum are compared. The maximum tangential stress (MTS) criterion, the minimum strain energy density (MSED) criterion and the new general fracture criterion based on the energy release rate G(θ) are investigated using advanced finite element technique. The displacement extrapolation technique (DET) is used, to obtain the SIFs at crack tip. Several examples are presented to show the robustness of the numerical techniques. The effect of the inclusions and cavities on the crack propagation in cement orthopedic are highlighted.

Numerical simulation of a crack emanating from a micro-cavity in the orthopedic cement by technical sub modeling of total hip prosthesis

“…In this study the mechanical properties of the components of the femoral prosthesis were taken from previous work [5,7,9,13,23].…”

“…In the cemented femoral prosthesis, the structural resistance of the THP is provided by the cement, which must withstand the mechanical stresses that can potentially lead to the generation and propagation of cracks and the possible failure of the entire THP structure [3,4]. PMMA has important micro structural heterogeneities such as cavities, and its elastic behavior is greatly affected by the presence of defects that may imply its weakening and cause failure [4,5]. In areas of high concentrations of stress and due to the presence of micro cracks appear after crushing cavities due to patient movement; these micro cracks grow and weld to each other until they form a macro fissure that propagates until the total removal of the prosthesis [6,7].…”

Strain Energy Density Prediction of Mixed-Mode Crack Propagation in Functionally Graded Materials

“…There are several techniques are used to obtain stress intensity factors (SIFs) in homogeneous and inhomogeneous materials, such as the displacement correlation technique (DCT) [20], the J* k -Integral [21,22] and the modified crack-closure integral (MCC) [23]. The displacement extrapolation technique (DET) used to calculate the SIFs K I and K II for homogeneous materials [24][25][26][27] is modified to calculate the SIFs for non-homogeneous materials, in present study. For the FGMs, the SIFs K I and K II can be expressed as follows:…”

Mechanical Behavior of Bone Cement under Dynamic Loading

“…This risk is due to the low tensile strength of the cement. Other numerical work [12] showed that the existence of microcavity promotes the initiation and propagation of cracks of the cup of cement. The stress intensity factor is strongly influenced by the nature of the bone-cement interface, cement-implant.…”

“…Several research works were dedicated to the analysis of the damage of the cement which is largely responsible for the loosening of the total hip prosthesis. So Mr. Bouziane et al [10] Zouambi et al [11], Benouis et al [12] analysed by the finite element method the effect of the microcavity on the behaviour of hip cement. These authors showed that these defects weaken the material due to notch effect and interaction.…”