School of Engineering, Computing and Mathematics
Faculty of Technology, Design and Environment
This paper presents an unified mathematical and computational framework for mechanics-coupled “anomalous” transport phenomena in porous media. The anomalous diffusion is mainly due to variable fluid flow rates caused by spatially and temporally varying permeability. This type of behaviour is described by a fractional pore pressure diffusion equation. The diffusion transient phenomena is significantly affected by the order of the fractional operators. In order to solve 3D consolidation problems of large scale structures, the fractional pore pressure diffusion equation is implemented in a finite element framework adopting the discretised formulation of fractional derivatives given by Grunwald–Letnikov (GL). Here the fractional pore pressure diffusion equation is implemented in the commercial software Abaqus through an open-source UMATHT subroutine. The similarity between pore pressure, heat and hydrogen transport is also discussed in order to show that it is possible to use the coupled thermal-stress analysis to solve fractional consolidation problems.
An innovative technique, called conversion, is introduced to model circumferential cracks in thin cylindrical shells. The semi-analytical finite element method is applied to investigate the modal deformation of the cylinder. An element including the crack is divided into three sub-elements with four nodes in which the stiffness matrix is enriched. The crack characteristics are included in the finite element method relations through conversion matrices and a rotational spring corresponding to the crack. Conversion matrices obtained by applying continuity conditions at the crack tip are used to transform displacements of the middle nodes to those of the main nodes. Moreover, another technique, called spring set, is represented based on a set of springs to model the crack as a separated element. Components of the stiffness matrix related to the separated element are incorporated while the geometric boundary conditions at the crack tip are satisfied. The effects of the circumferential mode number, the crack depth and the length of the cylinder on the critical buckling load are investigated. Experimental tests, ABAQUS modeling and results from literature are used to verify and validate the results and derived relations. In addition, the crack effect on the natural frequency is examined using the vibration analysis based on the conversion technique.
The knee meniscus is a highly porous structure which exhibits a grading architecture through the depth of the tissue. The superficial layers on both femoral and tibial sides are constituted by a fine mesh of randomly distributed collagen fibers while the internal layer is constituted by a network of collagen channels of a mean size of 22.14 μμm aligned at a 30∘30∘ inclination with respect to the vertical. Horizontal dog-bone samples extracted from different depths of the tissue were mechanically tested in uniaxial tension to examine the variation of elastic and viscoelastic properties across the meniscus. The tests show that a random alignment of the collagen fibers in the superficial layers leads to stiffer mechanical responses (E = 105 and 189 MPa) in comparison to the internal regions (E = 34 MPa). All regions exhibit two modes of relaxation at a constant strain (τ1=6.4τ1=6.4 to 7.7 s, τ2τ2 = 49.9 to 59.7 s).
The meniscus is an integral part of the human knee, preventing joint degradation by distributing load from the femoral condyles to the tibial plateau. Recent qualitative studies suggested that the meniscus is constituted by an intricate net of collagen channels inside which the fluid flows during loading. The aim of this study is to describe in detail the structure in which this fluid flows by quantifying the orientation and morphology of the collagen channels of the meniscal tissue. A 7 mm cylindrical sample, extracted vertically from the central part of a lateral porcine meniscus was freeze-dried and scanned using the highest-to-date resolution Microscopic Computed Tomography. The orientation of the collagen channels, their size and distribution was calculated. Comparisons with confocal multi-photon microscopy imaging performed on portions of fresh tissue have shown that the freeze-dried procedure adopted here ensures that the native architecture of the tissue is maintained. Sections of the probe at different heights were examined to determine differences in composition and structure along the sample from the superficial to the internal layers. Results reveal a different arrangement of the collagen channels in the superficial layers with respect to the internal layers with the internal layers showing a more ordered structure of the channels oriented at 30∘∘ with respect to the vertical, a porosity of 66.28% and the mean size of the channels of 22.14 μmμm.
This paper presents a slicing technique useful to prepare precise and repeatable samples from organs which are irregularly shaped and highly heterogeneous for mechanical testing and advanced microscopy observation. The suggested technique does not seem to influence the internal microstructure and it is employed here for testing specimens cut from different region of the meniscal tissue. Fast Fourier Transform analysis is used to quantify characteristic features of the microstructure (collagen fibers orientation, pore size) after slicing prior mechanical testing. Uniaxial (relaxation) tests are performed on dog-bone meniscal samples. Stress relaxation testing results on samples cut from different regions of the meniscus highlights a significant scatter in the maximum stress even though the preferential collagen fibers orientation is not too dissimilar. The proposed slicing method, which requires inexpensive tools and allows to minimize sample preparation, is proved to be applicable for a range of applications from macroscopic/nano mechanical testing to microscopy observations to accurately characterize location-dependent microstructural features and mechanical properties.
In this paper we present the results from a recent micromechanical investigation aimed at developing methodologies for testing and understanding the fundamental behaviour of meniscal tissue. To achieve this, we employed two distinctly different, but equally relevant mechanical testing platforms – uniaxial tensile testing and Dynamic Mechanical Analysis. The results from the tensile tests revealed that the studied material exhibits non-linear stress-strain behaviour and that its viscoelastic properties are timedependent. Furthermore, by using DMA it was possible to perform walking and running simulations, which provided furtherinformation of the strain=time response of the meniscal samples. The importance of accurate specimen preparation and actual method development are also presented and discussed in detail.
The complex inhomogeneous architecture of the human meniscal tissue at the micro and nano scale in the absence of artefacts introduced by sample treatments has not yet been fully revealed. The knowledge of the internal structure organization is essential to understand the mechanical functionality of the meniscus and its relationship with the tissue’s complex structure. In this work, we investigated human meniscal tissue structure using up-to-date non-invasive imaging techniques, based on multiphoton fluorescence and quantitative second harmonic generation microscopy complemented with Environmental Scanning Electron Microscopy measurements. Observations on 50 meniscal samples extracted from 6 human menisci (3 lateral and 3 medial) revealed fundamental features of structural morphology and allowed us to quantitatively describe the 3D organisation of elastin and collagen fibres bundles. 3D regular waves of collagen bundles are arranged in “honeycomb-like” cells that are comprised of pores surrounded by the collagen and elastin network at the micro-scale. This type of arrangement propagates from macro to the nanoscale.
Finite element analysis of linear-elastic structures with spatially varying uncertain properties is addressed within the framework of the interval model of uncertainty. Resorting to a recently proposed interval field model, the uncertain properties are expressed as the superposition of deterministic basis functions weighted by particular unitary intervals. An Interval Finite Element Method (IFEM) incorporating the interval field representation of uncertainties is formulated by applying an interval extension in conjunction with the standard energy approach. Uncertainty propagation analysis is performed by adopting a response surface approach which provides approximate explicit expressions of response bounds requiring only a few deterministic analyses. Then, the whole procedure is implemented in ABAQUS’ environment by coding User Subroutines and Python scripts.
2D plane stress and bending problems involving uncertain Young's modulus of the material are analyzed. The accuracy of the proposed IFEM as well as response variability under spatially dependent uncertainty are investigated.
The meniscus plays a critical role in load transmission, stability and energy dissipation in the knee joint. Loss of the meniscus leads to joint degeneration and osteoarthritis. In a number of cases replacement of the resected meniscal tissue by a synthetic implant might avoid the articular cartilage degeneration. None of the available implants presents optimal biomechanics characteristic due to the fact the biomechanics functionality of the meniscus is not yet fully understood. Mimicking the native biomechanical characteristics of the menisci seems to be the key factor in meniscus replacement functioning. This is extremely challenging due to its complex inhomogeneous microstructure, the lack of a full experimental characterization of the material properties and the lack of 3D theoretical, numerical and computational models which can reproduce and validate the experimental results. The objective of this work is to present the experimental characterization of the anisotropic meniscal tissue at the macroscale. Innovative Biaxial tests have been conducted and the results are new to the literature.