Hamid Nayeb-Hashemi

Effect of frontal plane tibiofemoral angle on the stress and strain at the knee cartilage during the stance phase of gait

Subject‐specific three‐dimensional finite element models of the knee joint were created and used to study the effect of the frontal plane tibiofemoral angle on the stress and strain distribution in the knee cartilage during the stance phase of the gait cycle. Knee models of three subjects with different tibiofemoral angle and body weight were created based on magnetic resonance imaging of the knee. Loading and boundary conditions were determined from motion analysis and force platform data, in conjunction with the muscle‐force reduction method. During the stance phase of walking, all subjects exhibited a valgus–varus–valgus knee moment pattern with the maximum compressive load and varus knee moment occurring at approximately 25% of the stance phase of the gait cycle. Our results demonstrated that the subject with varus alignment had the largest stresses at the medial compartment of the knee compared to the subjects with normal alignment and valgus alignment, suggesting that this subject might be most susceptible to developing medial compartment osteoarthritis (OA). In addition, the magnitude of stress and strain on the lateral cartilage of the subject with valgus alignment were found to be larger compared to subjects with normal alignment and varus alignment, suggesting that this subject might be most susceptible to developing lateral compartment knee OA.

The Combined Effect of Frontal Plane Tibiofemoral Knee Angle and Meniscectomy on the Cartilage Contact Stresses and Strains

Abnormal tibiofemoral alignment can create loading conditions at the knee that may lead to the initiation and progression of knee osteoarthritis (OA). The degenerative changes of the articular cartilage may occur earlier and with greater severity in individuals with abnormal frontal plane tibiofemoral alignment who undergo a partial or total meniscectomy. In this investigation, subject specific 3D finite element knee models were created from magnetic resonance images of two female subjects to study the combined effect of frontal plane tibiofemoral alignment and total and partial meniscectomy on the stress and strain at the knee cartilage. Different amounts of medial and lateral meniscectomies were modeled and subject specific loading conditions were determined from motion analysis and force platform data during single-leg support. The results showed that the maximum stresses and strains occurred on the medial tibial cartilage after medial meniscectomy but a greater percentage change in the contact stresses and strains occurred in the lateral cartilage after lateral meniscectomy for both subjects due to the resultant greater load bearing role of the lateral meniscus. The results indicate that individual’s frontal plane knee alignment and their unique local force distribution between the cartilage and meniscus play an important role in the biomechanical effects of total and partial meniscectomy.

Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state.

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

Protocol for constructing subject-specific biomechanical models of knee joint

A robust protocol for building subject-specific biomechanical models of the human knee joint is proposed which uses magnetic resonance imaging, motion analysis and force platform data in conjunction with detailed 3D finite element models. The proposed protocol can be used for determining stress and strain distributions and contact kinetics in different knee elements at different body postures during various physical activities. Several examples are provided to highlight the capabilities and potential applications of the proposed protocol. This includes preliminary results on the role of body weight on the stresses and strains induced in the knee articular cartilages and meniscus during single-leg stance and calculations of the induced stresses and ligament forces during the gait cycle.

Mixed mode I/II fracture and fatigue crack growth along 63Sn-37Pb solder/brass interface

Abstract Solder joints are extensively used in electronic packaging. They provide critical electrical and mechanical connections. Single edge notched sandwich specimens, which were made of two blocks of brass joined with a 63Sn–37Pb solder layer, were prepared for a fatigue and fracture study of the joint under mixed mode loading. Mode I and mixed mode I/II fracture toughness, fatigue crack thresholds, and fatigue crack growth rates (FCGR) were measured at room temperature using a four point bending test setup. It was found that the fracture toughness of the joint increased and FCGR decreased upon the introduction of the mode II component. The interface fracture toughness was higher than that reported for pure solder. The data of FCGR correlated well with the power law relation of d a/ d N=C ∗ (ΔG) m , where ΔG is the alternating energy released rate for a crack under mixed mode loading. It was also observed that both fracture toughness and FCGR were a function of the solder layer thickness. When the solder layer thickness increased from 0.1 to 1.0 mm, the fracture toughness decreased substantially and FCGR increased slightly. For mode I loading, fatigue cracks propagated inside the solder layer. However, for mixed mode loading, once a crack initiated, it changed its direction toward the interface and then propagated along the interface. These observations were related to local mode I and mode II stress fields. Fracture surfaces showed signs of rubbing under mixed mode loading with elongated cavities at the crack tip. However, under mode I loading, fracture surfaces were covered with equi-ax voids.

Multiaxial fatigue life evaluation of tubular adhesively bonded joints

Abstract The only viable method for joining plastic tubes and composite shafts is by bonding them adhesively. These structures are often subjected to complex cyclic loadings. Failure of these tubular joints not only depends on the applied loads, but also depends on the tube geometry, material properties of adhesive and tubes, and defects in the joint. The shear stress distribution in the tubular joints is obtained for joints under axial and torsional loadings using the shear lag model. Under axial loading the adhesive is assumed to carry only shear stress and adherend to carry only axial load. However, the model considers the variation of the shear stress across the adhesive thickness. The effect of a void on the maximum shear stress is obtained. A nondimensional θa parameter is defined and it is shown that the shear stress distribution not only depends on the value of θa but it also depends on cross sectional geometry of the tubes. For tubes with equal cross sectional area, the shear stress distribution along the bonded area is almost symmetric. For tubular joints with θa equal or greater than 6.7, a centrally symmetrical annular void with a size of at least 50% of the overlap length has little effect on the maximum shear stress and thus the failure load. The shear stress under torsional loading is obtained by assuming the adhesive to shear in the circumferential direction only and neglecting its other deformations. The tubes are assumed to shear in the axial direction. The analysis considers the variation of the shear stress across the adhesive thickness. As in the case of axial loading, a new nondimensional parameter, θt for tubes under torsion is defined. The results show that the shear stress in the bonded area not only depends on the 0, value, but also depends on the polar moment of inertia, J1 and J2, of the tubes. The effect of annular voids on the shear stress distribution is evaluated for different void sizes and θt values. The failure locus of adhesively bonded tubular specimens under axial, torsional and combined axial and torsional loadings is obtained. Based on these results a damage model for the tubular joints under combined axial and torsional cyclic loading is proposed. It is shown that this model can predict the fatigue life of the tubular joints reasonably well.

Dynamic response of tubular joints with an annular void subjected to a harmonic axial load

Abstract Dynamic responses of adhesively bonded tubular joints subjected to a harmonic axial load were evaluated with the use of a shear lag model. Adherents were assumed to be elastic and the adhesive was taken to be a viscoelastic material. Effects of tubular joint geometries, material properties and adhesive properties on the dynamic response of the system were investigated. The results showed that the system response was sensitive to the adhesive loss factor. The system response was little affected by the presence of a central annular void in the bond area for void size less than 40% of the overlap length. This was especially pronounced for joints using adhesives with a larger loss factor (viscous damping). The distribution of shear stress amplitude in the joint area was obtained. The maximum shear stress was confined to the edge of the overlap for all applied loading frequencies. For the adhesive and adherents’ properties and geometries investigated, the maximum shear stress amplitude in the joint area was little affected by the presence of a central annular void covering up to 40% of the overlap length. However, for a void larger than 40% of the overlap length, the maximum shear stress might increase or decrease with an increase in the void size. This was related to the applied loading frequency and the changes in the system resonance frequencies.

Finite element modeling following partial meniscectomy: Effect of various size of resection

Meniscal tears are a common occurrence in the human knee joint. Orthopaedic surgeons routinely perform surgery to remove a portion of the torn meniscus. This surgery is referred to as a partial meniscectomy. It has been shown that individuals who have decreased amount of meniscus are likely to develop knee osteoarthritis. This research presents the analysis of the stresses in the knee joint upon various amounts of partial meniscectomy. To analyse the stresses in the knee joint using finite element method an axisymmetric model was developed. Articular cartilage was considered as three layers, which were modelled as a poroelastic transversely isotropic superficial layer, a poroelastic isotropic middle and deep layers and an elastic isotropic calcified cartilage layer. Eight cases were modelled including a knee joint with an intact meniscus, 10%, 20%, 30%, 40%, 50%, 60% and 65% medial meniscotomy. Under the axial load of human weight on the femoral articular cartilage with 40% removal of meniscus high contact stresses took place on cartilage surface. Further, with 30%, 40%, 50% of meniscectomy significant amount of contact area noticed between femoral and tibial articular cartilage. After 65% of meniscectomy the maximal shear stress in the cartilage increased up to 225% compared to knee with intact meniscus. It appears that meniscectomies greater than 20% drastically increases the stresses in the knee joint

Comparison of the Effects of Debonds and Voids in Adhesive Joints

An analytical model is developed to compare the effects of voids and debonds on the interfacial shear stresses between the adherends and the adhesive in simple lap joints. Since the adhesive material above the debond may undergo some extension (either due to applied load or thermal expansion or both), a modified shear lag model, where the adhesive can take on extensional as well as shear deformation, is used in the analysis. The adherends take on only axial loads and act as membranes. Two coupled nondimensional differential equations are derived, and in general, five parameters govern the stress distribution in the overlap region. As expected, the major differences between the debond and the void occur for the stresses near the edge of the defect itself. Whether the defect is a debond or a void, is hardly discernible by the stresses at the overlap ends for central defect sizes up to the order of 70 percent of the overlap region. If the defect occurs precisely at or very close to either end of the overlap, however, differences of the order of 20 percent in the peak stresses can be obtained.

Constitutive relations and fatigue life prediction for anisotropic Al-6061-T6 rods under biaxial proportional loadings

Abstract Cyclic stress-strain curves (CSSCs) and fatigue lives were obtained from fully reversed fatigue tests in strain control on two anisotropic Al-6061-T6 rods. The experiments were conducted at room temperature under three types of loading conditions: tension-compression, torsion and combined proportional tension-torsion. Based on the CSSC data, the anisotropic constitutive relations of the rods were obtained by using Hills anisotropic plasticity theory. Yield loci and flow behaviour were determined and compared with the theoretical predictions. Two anisotropic effective-stress-effective-strain criteria were evaluated. During the fatigue tests the fatigue cracking behaviour of the rods was observed and found to be shear dominated. Four multiaxial fatigue life prediction models representing three different concepts were used to correlate the fatigue life data. A shear cracking model incorporated with a material anisotropy constant correlated with the test data very well. The other models, however, gave poor correlations.