Antoni John

Prediction of Young׳s modulus of trabeculae in microscale using macro-scale׳s relationships between bone density and mechanical properties.

According to the literature, there are many mathematical relationships between density of the trabecular bone and mechanical properties obtained in macro-scale testing. In micro-scale, the measurements provide only the ranges of Young׳s modulus of trabeculae, but there are no experimentally tested relationships allowing the calculation of the distribution of Young׳s modulus of trabeculae within these experimental ranges. This study examined the applicability of relationships between bone density and mechanical properties obtained in macro-scale testing for the calculation of Young׳s modulus distribution in micro-scale. Twelve cubic specimens from eleven femoral heads were cut out and micro-computed tomography (micro-CT) scanned. A mechanical compression test and Digital Image Correlation (DIC) measurements were performed to obtain the experimental displacement and strain full-field evaluation for each specimen. Five relationships between bone density and Young׳s modulus were selected for the test; those were given by Carter and Hayes (1977), Ciarelli et al. (2000), Kaneko et al. (2004), Keller (1994) for the human femur, and Li and Aspden, 1997. Using these relationships, five separate finite element (FE) models were prepared, with different distribution of Young׳s modulus of trabeculae for each specimen. In total, 60 FE analyses were carried out. The obtained displacement and strain full-field measurements from numerical calculations and experiment were compared. The results indicate that the highest accuracy of the numerical calculation was obtained for the Ciarelli et al. (2000) relationship, where the relative error was 17.87% for displacements and 50.94 % for strains. Therefore, the application of the Ciarelli et al. (2000) relationship in the microscale linear FE analysis is possible, but mainly to determine bone displacement.

Numerical Analysis of Solid and Shell Models of Human Pelvic Bone

Numerical modeling of human pelvic bone makes possibilities to determine the stress and strain distribution in bone tissue. The general problems are: complex geometry, material structure and boundary conditions. In the present paper some simplifications in numerical model are performed. Homogeneous elastic properties of bone tissue are assumed. The shell model and solid model of pelvic bone are analyzed. The finite element method is applied. Some numerical results for solid and shell model are presented.

Image-based finite element modeling of the three-point bending test of cortical bone

The numerical simulation of the response of bone tissue to loading is a very common method in the biomedical engineering. The high diversity of bone quality, fractures and metabolic diseases, requires different approaches to numerical simulation. The main aim of this study was image-based finite element modeling (FEM) of the three-point bending tests of cortical bone. The results from the simulation performed based on own materials can be then used to non-destructive prediction of the bone mechanical strength. The samples were scanned by X-ray microcomputed tomography (XMT). Grey values of the imaged phantom were calibrated to known values of the phantom densities. It enabled estimation of the calibration curve for mineral level in bone, that was further applied to the calculation of bone density and the estimation of the material parameters in the FE model. In one example, the finite element analysis gives the deflection y=0.7 mm that match results from experiments where deflection was equal to y =0,69mm. The reported studies delivered useful data for future prediction of the mechanical parameters based on only imaging data.

FEM in Numerical Analysis of Stress and Displacement Distributions in Planetary Wheel of Cycloidal Gear

Implementation of high speed engines requires application of high ratio mechanical gears. Relatively, the smallest mechanical gear is the cycloidal planetary gear known as Cyclo gear [2, 8- 11]. The complex construction of planet wheels in cycloidal planetary gear (Cyclo) practically makes impossible its optimal design. To calculate distribution of displacements and stresses in planet wheels with cooperating elements FEM has been implemented. There were series of numerical models of planet wheels generated and for example of real model of gear it has been calculated proper values of forces, strains and stresses. In the paper forces and strains calculated with FEM have been used to check the assumptions which have been applied only in analytical so far.

The Inverse Honeycomb Structures in Numerical Modeling and Experiment

Based on previous research, we proposed changes in the classic honeycomb structure. We have changed the approach to modeling. In a classic structure, cells are modeled using the walls that form them. In the modified structure, the main modeled element is the hexagon-shaped void. The distribution of cells was proposed as in a truss. In full places the spaces were smaller and in empty places the cells were larger. We changed the size of cells and the transition between cells in different layers. In comparison to previous research, it was necessary to enlarge the models. This was due to the limitations of incremental technology, which was used to fabricate samples – FDM. This technology introduced limitations of changes that the structure underwent. We selected several types of models as a result of the numerical simulation and produced. Then, experimental tests were carried out on them – the same as in numerical simulation. In the final stage, we compared the obtained results. DOI: http://dx.doi.org/10.5755/j01.mech.24.3.21066

The foamed structures in numerical testing

In the paper numerical simulation of the foamed metal structures using numerical homogenization algorithm is prescribed. From the beginning, numerical model of heterogeneous porous simplified structures of typical foamed metal, based on the FEM was built and material parameters (coefficients of elasticity matrix of the considered structure) were determined with use of numerical homogenization algorithm. During the work the different RVE models of structure were created and their properties were compared at different relative density, different numbers and the size and structure of the arrangement of voids. Finally, obtained results were used in modeling of typical elements made from foam metals structures - sandwich structure and profile filled with metal foam. Simulation were performed for different dimensions of cladding and core. Additionally, the test of influence material orientation (arrangement of voids in RVE element) on the maximum stresses and displacement during bending test was performed.

Numerical examination of like-honeycomb structures

In the paper based on the analogy with the biological tissue of bones, it was decided to examine more homogenous structure and also a heterogeneous structure too. Here, a new approach is proposed based on results from literature obtained using topology optimization 2D and 3D structures like beam, girder and cantilever. Proposed model of structure is similar to spatial trusses with honeycomb-shape porous. Parameters varied not only uniformly throughout the volume of the sample, but also be modified depending on various factors. They underwent a change in cell dimensions, among other things, the thickness of the wall. The obtained results were compared with those obtained previously for homogeneous samples.

Microscale’s relationship between Young’s modulus and tissue density. Prediction of displacements

Abstract The study presents an experimental verification of Wagner et al.’s relationship in microscale and proposes a modification of this relationship. For this purpose, 11 cubic specimens were microcomputed tomography scanned and mechanically tested with the displacement full-field measurements using a digital image correlation system. Then, numerical simulations of the compression tests were performed using a finite elements method. The Young’s modulus distributions assigned to the finite elements models were calculated using both of Wagner et al.’s relationships: original and modified. Comparison of the experimental and numerical results indicated the accuracy of numerical solutions for both relationships.

Numerical Simulation of the Foamed Metal Structures

In this paper, multi-scale modelling of the foamed metal structures using numerical homogenization algorithm is prescribed. First, a numerical model of heterogeneous porous simplified structures of typical foamed metal based on the FEM was built. Next, a micro-RVE model representing elementary volume of macroscopic model was constructed. Material parameters of the considered structure were determined with the use of numerical homogenization algorithm. In this work, the different RVE models of structure were created and their properties were compared at different relative density, different numbers, and the size and structure of the arrangement of voids. Finally, obtained results were used in modelling of typical elements made from foam metals structures-reinforced profile and sandwich structures. Simulations were performed for different dimensions of cladding and core.

Numerical Testing of Honeycomb Structures

In this paper, modeling and numerical analysis of mechanical parameters of honeycomb structures are presented for application in sandwich structures. Parametrical model of honeycomb structures was built and next numerical simulation for different configuration of cell size and different boundary conditions were performed. One wanted to see whether in this case the added cladding significantly affect the improvement in results. Along with another simulation changed the size and type of grid computing. In this, case when the grid consisted of larger items, the results obtained were satisfactory. Along with reducing components—increase the accuracy of calculations—significant changes were observed in the obtained results. In subsequent step, it was decided to see how the structure will behave when the core will consist of several layers of cells shifted relative to each other. Finally, sandwich structure during mechanical test was simulated.