Elisa Budyn

A method for growing multiple cracks without remeshing and its application to fatigue crack growth

A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.

Multiple scale modeling for cortical bone fracture in tension using X-FEM

We present a multiple scale method for modeling multiple crack growth in cortical bone under tension. The four phase composite Haversian microstructure is discretized by a Finite Element Method. The geometrical and mechanical bone parameters obtained by experiments mimic the heterogeneity of bone at the micro scale. The cracks are initiated at the micro scale where a critical elastic-damage strain driven criterion is met and are grown until complete failure in heterogeneous linear elastic media when a critical stress intensity factor criterion is reached. The cracks are modeled by the eXtended Finite Element Method. The simulations provide the global response at the macroscopic level and stress and strain fields at the microscopic level. The model emphasizes the importance of the microstructure on bone failure in assessing the fracture risk.

Analysis of micro fracture in human Haversian cortical bone under compression

A procedure to investigate local stress intensity factors in human Haversian cortical bone under compression is presented. The method combines a customised experimental setting for micro-compression tests of millimetric bone specimens and a finite element contact model conforming to the bone morphology that tracks advancing microcracks. The non-interpenetration conditions along the crack edges are ensured by penalty constraints of which the parameters are optimised for minimum contact pressure error with respect to the crack orientations. A cohesive crack opening law is implemented in the wake of the crack tips to remain consistent with the progressive tearing of collagen fibrils. The displacement solution is searched by a Newton-Raphson scheme containing a double loop first on the displacements and second on the frictional contact and cohesive condition updates at the crack interfaces. The experimental Dirichlet boundary conditions are acquired by digital image cross-correlation of bone light microscopy observations and then imported into the model. The local mechanical elastic moduli are measured by nanoindentation and microextensometry. The comparison of the macroscopic stress-strain numerical response with the experiment reveals the existence of narrow diffuse damaged zones near the major cracks where the local stress intensity factors can be calculated.

Microdomain heterogeneity in 3D affects the mechanics of neonatal cardiac myocyte contraction.

Cardiac muscle cells are known to adapt to their physical surroundings, optimizing intracellular organization and contractile function for a given culture environment. A previously developed in vitro model system has shown that the inclusion of discrete microscale domains (or microrods) in three dimensions (3D) can alter long-term growth responses of neonatal ventricular myocytes. The aim of this work was to understand how cellular contact with such a domain affects various mechanical changes involved in cardiac muscle cell remodeling. Myocytes were maintained in 3D gels over 5 days in the presence or absence of 100−μm-long microrods, and the effect of this local heterogeneity on cell behavior was analyzed via several imaging techniques. Microrod abutment resulted in approximately twofold increases in the maximum displacement of spontaneously beating myocytes, as based on confocal microscopy scans of the gel xy-plane or the myocyte long axis. In addition, microrods caused significant increases in the proportion of aligned myofibrils (≤20° deviation from long axis) in fixed myocytes. Microrod-related differences in axial contraction could be abrogated by long-term interruption of certain signals of the RhoA-/Rho-associated kinase (ROCK) or protein kinase C (PKC) pathway. Furthermore, microrod-induced increases in myocyte size and protein content were prevented by ROCK inhibition. In all, the data suggest that microdomain heterogeneity in 3D appears to promote the development of axially aligned contractile machinery in muscle cells, an observation that may have relevance to a number of cardiac tissue engineering interventions.

High resolution volume quantification of the knee joint space based on a semi-automatic segmentation of computed tomography images

Osteoarthritis (OA) is a joint disorder that causes pain, stiffness and decreased mobility. Knee OA presents the greatest morbidity. The main characteristic of OA is the cartilage loss inducing joint space (JS) narrowing. Usually, the progression of OA is monitored by the minimum JS measurement on 2D X-rays images. New dedicated systems based on cone beam computed tomography, providing enough image quality and with favourable dose characteristics are under development. With these new systems, it would be possible to follow the 3D JS changes. High resolution peripheral computed tomography (HR-pQCT) usually used for assessing the trabecular and cortical bone mineral density have been performed on specimen knees with an isotropic voxel of 82 microns. We present here a new semi-automatic segmentation method to measure the 3D local variations of JS. The experiments have been done on HR-pQCT data set and the results have been extended to other computed tomography images with low resolution and/or with cone beam geometry.

Microextensometry and mechanical behaviour of Haversian cortical bone

It is well known that bone microarchitecture is mainly the result of the bone remodelling process. However, a mechanistic framework describing how the microstructure affects the mechanical behaviour of bone is still lacking. Therefore, tools to quantify bone quality at the microstructure scale are required. To address this problem, the present study focused on the measurements of the local strains over a large microstructure area using microextensometry. First, the relationship between the local strains and the mineral content was examined. Then, the local strains were used to feed an inverse approach performed by finite elements. The results show there is no correlation between the strain and the mineral content. Moreover, the implementation of the mineral content in finite elements simulations gave a better estimate of the experimental strain field.

Multiple Crack Growth failure in Cortical Bone under Tension by the eXtended Finite Element Method

A multi-scale analysis for multiple crack growth in unit cell of cortical bone is presented. The cracks are grown until complete failure of the cell. The initial cracks are placed in maximum strain locations. The stress intensity factors are computed at each crack tip and a load parameter is adjusted so that the stress intensity factors remain at the critical value. In the case of competitive crack tips, a stability analysis is performed by computing the second derivative of the potential energy for each crack. The load deflection behavior of the representative volume element is obtained until the point of complete failure. The model is fed with experimental geometrical, mechanical and damage parameters and validated through a comparison with experimental samples. The discretization utilizes the eXtended Finite Element Method and requires no remeshing as the cracks grow. The crack geometries are arbitrary with respect to the mesh, and are described by a vector level set. Special boundary conditions and the algorithm for detecting crack bridging and crack entering Haversian canals which allows the cracks to grow ntil maximum failure and/or percolation is presented. Open image in new window

The Effects of Porosity Changes on Aging Cortical Bone Mechanics Using an Evolutionary Monte Carlo Algorithm

Human Haversian cortical bone has a composite microstructure that is reinforced with hollowed long fibers called osteons. The biological tissue is highly heterogeneous and changes with age. Following hormonal modifications, osteoporosis is developed by nearly a third of women over 65 and the pathology significantly increases bone porosity. Treatments using biphosphonates to slow down the excessive bone resorption can lead to a reduced osteon counts. We present a study of relevant morphological parameters to characterise pathological microstructural evolutions of bone and we detail its implementation into Monte Carlo synthetic bone 3D microstructures. The results are validated against explicit real bone models and show the effects of either a porosity increase or a fiber content reduction on the internal strain distribution.

Multiresolution Mechanics for Nano/Micro-Structured Materials

To understand the mechanics of materials, it is important to faithfully model the physics due to interactions at the microstructural scales. While brute-force modeling of all the details of the microstructure is too costly, current homogenized continuum models suffer from their inability to sufficiently capture the correct physics - especially where localization and failure are concerned.

Micro-Mechanical Characterisation of Human Cortical Bone

We present a numerical model to mechanically characterise real and Monte-Carlo microstructures of human cortical bone. Femoral mid-shaft human bone microstructures are specific to each individual and exhibit unique morphological and mechanical properties. Real microstructures of female bone samples are explicitly reconstructed using a finite element model. Patient-dependent statistically equivalent models are built from natural morphological parameters measured under reflected light microscopy (RLM) and back-scattered electron microscopy (BSEM). The micro mechanical properties are provided by nanoindentations and microextensometry. The morphological and mechanical characteristics are incorporated into the model to mimic bone micro-scale heterogeneity. The overall stiffness of the microstructure is calculated for a distribution of samples. The effects of the variations of local parameters on the global stiffness are studied. The evolution of these parameters indicates various aging signs of bone. These results are validated through comparison to experiments to assess fracture risk.Copyright