Local stress-strain distribution and load transfer across cartilage matrix at micro-scale using combined microscopy-based finite element method

Articular cartilage is the load-bearing tissue that consists of proteoglycan macromolecules entrapped between collagen fibrils in a three-dimensional architecture. To date, the drudgery of searching for mathematical models to represent the biomechanics of such a system continues without providing a fitting description of its functional response to load at micro-scale level. We believe that the major complication arose when cartilage was first envisaged as a multiphasic model with distinguishable components and that quantifying those and searching for the laws that govern their interaction is inadequate. To the thesis of this paper, cartilage as a bulk is as much continuum as is the response of its components to the external stimuli. For this reason, we framed the fundamental question as to what would be the mechano-structural functionality of such a system in the total absence of one of its key constituents-proteoglycans. To answer this, hydrated normal and proteoglycan depleted samples were tested under confined compression while finite element models were reproduced, for the first time, based on the structural microarchitecture of the cross-sectional profile of the matrices. These micro-porous in silico models served as virtual transducers to produce an internal noninvasive probing mechanism beyond experimental capabilities to render the matrices micromechanics and several others properties like permeability, orientation etc. The results demonstrated that load transfer was closely related to the microarchitecture of the hyperelastic models that represent solid skeleton stress and fluid response based on the state of the collagen network with and without the swollen proteoglycans. In other words, the stress gradient during deformation was a function of the structural pattern of the network and acted in concert with the position-dependent compositional state of the matrix. This reveals that the interaction between indistinguishable components in real cartilage is superimposed by its microarchitectural state which directly influences macromechanical behavior.

Numerical simulations of particle deposition in metal foam heat exchangers

Australia is a high-potential country for geothermal power with reserves currently estimated in the tens of millions of petajoules, enough to power the nation for at least 1000 years at current usage. However, these resources are mainly located in isolated arid regions where water is scarce. Therefore, wet cooling systems for geothermal plants in Australia are the least attractive solution and thus air-cooled heat exchangers are preferred. In order to increase the efficiency of such heat exchangers, metal foams have been used. One issue raised by this solution is the fouling caused by dust deposition. In this case, the heat transfer characteristics of the metal foam heat exchanger can dramatically deteriorate. Exploring the particle deposition property in the metal foam exchanger becomes crucial. This paper is a numerical investigation aimed to address this issue. Two dimensional (2D) numerical simulations of a standard one-row tube bundle wrapped with metal foam in cross-flow are performed and highlight preferential particle deposition areas.

A stochastic thermostat algorithm for coarse-grained thermomechanical modeling of large-scale soft matters : theory and application to microfilaments

As all-atom molecular dynamics method is limited by its enormous computational cost, various coarse-grained strategies have been developed to extend the length scale of soft matters in the modeling of mechanical behaviors. However, the classical thermostat algorithm in highly coarse-grained molecular dynamics method would underestimate the thermodynamic behaviors of soft matters (e.g. microfilaments in cells), which can weaken the ability of materials to overcome local energy traps in granular modeling. Based on all-atom molecular dynamics modeling of microfilament fragments (G-actin clusters), a new stochastic thermostat algorithm is developed to retain the representation of thermodynamic properties of microfilaments at extra coarse-grained level. The accuracy of this stochastic thermostat algorithm is validated by all-atom MD simulation. This new stochastic thermostat algorithm provides an efficient way to investigate the thermomechanical properties of large-scale soft matters.

A simulation-based large deflection and inelastic analysis of steel frames under fire

This paper presents an accurate and robust geometric and material nonlinear formulation to predict structural behaviour of unprotected steel members at elevated temperatures. A fire analysis including large displacement effects for frame structures is presented. This finite element formulation of beam-column elements is based on the plastic hinge approach to model the elasto-plastic strain-hardening material behaviour. The Newton-Raphson method allowing for the thermal-time dependent effect was employed for the solution of the non-linear governing equations for large deflection in thermal history. A combined incremental and total formulation for determining member resistance is employed in this nonlinear solution procedure for the efficient modeling of nonlinear effects. Degradation of material strength with increasing temperature is simulated by a set of temperature-stress-strain curves according to both ECCS and BS5950 Part 8, which implicitly allows for creep deformation. The effects of uniform or non-uniform temperature distribution over the section of the structural steel member are also considered. Several numerical and experimental verifications are presented.

Nonlinear pre-fire and post-fire analysis of steel frames

A numerical procedure based on the plastic hinge concept for study of the structural behaviour of steel framed structures exposed to fire is described. Most previous research on fire analysis considered the structural performance due to rising temperature. When strain reversal occurs during the cooling phase, the stress–strain curve is different. The plastic deformation is incorporated into the stress–strain curve to model the strain reversal effect in which unloading under elastic behaviour is allowed. This unloading response is traced by the incremental–iterative Newton–Raphson method. The mechanical properties of the steel member in the present fire analysis follows both Eurocode 3 Part 1.2 and BS5950 Part 8, which implicitly allow for thermal creep deformation. This paper presents an efficient fire analysis procedure for predicting thermal and cooling effects on an isolated element and a multi-storey frame. Several numerical and experimental examples related to structural behaviour in cooling phase are studied and compared with results obtained by other researchers. The proposed method is effective in the fire safety design and analysis of a building in a real fire scenario. The scope of investigation is of great significance since a large number of rescuers would normally enter a fire site as soon as the fire is extinguished and during the cooling phase, so a structural collapse can be catastrophic.

Numerical study of lid-driven square cavity with heat generation using LBM

In this study, the mixed convection heat transfer and fluid flow behaviors in a lid-driven square cavity filled with high Prandtl number fluid (Pr = 5400, ν = 1.2×10-4 m2/s) at low Reynolds number is studied using thermal Lattice Boltzmann method (TLBM) where ν is the viscosity of the fluid. The LBM has built up on the D2Q9 model and the single relaxation time method called the Lattice-BGK (Bhatnagar-Gross-Krook) model. The effects of the variations of non dimensional mixed convection parameter called Richardson number(Ri) with and without heat generating source on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles as well as stream function and temperature contours for Ri ranging from 0.1 to 5.0 with other controlling parameters that present in this study. It is found that LBM has good potential to simulate mixed convection heat transfer and fluid flow problem. Finally the simulation results have been compared with the previous numerical and experimental results and it is found to be in good agreement.

Investigation on mechanical behaviour of AM60 magnesium alloys

Purpose: In this work, tension, impact, bend and fatigue tests were conducted in an AM60 magnesium alloy. The effects of environmental temperature and loading rates on impact and tension behavior of the alloy were also investigated. Design/methodology/approach: The tests were conducted using an Instron universal testing machine. The loading speed was changed from 1 mm/min to 300 mm/min to gain a better understanding of the effect of strain rate. To understand the failure behavior of this alloy at different environmental temperatures, Charpy impact test was conducted in a range of temperatures (-40~35°C). Plane strain fracture toughness (KIC) was evaluated using compact tension (CT) specimen. To gain a better understanding of the failure mechanisms, all fracture surfaces were observed using scanning electron microscopy (SEM). In addition, fatigue behavior of this alloy was estimated using tension test under tension-tension condition at 30 Hz. The stress amplitude was selected in the range of 20~50 MPa to obtain the S-N curve. Findings: The tensile test indicated that the mechanical properties were not sensitive to the strain rates applied (3.3x10-4~0.1) and the plastic deformation was dominated by twining mediated slip. The impact energy is not sensitive to the environmental temperature. The plane strain fracture toughness and fatigue limit were evaluated and the average values were 7.6 MPa.m1/2 and 25 MPa, respectively. Practical implications: Tested materials AM60 Mg alloy can be applied among others in automotive industry aerospace, communication and computer industry. Originality/value: Many investigations have been conducted to develop new Mg alloys with improved stiffness and ductility. On the other hand, relatively less attention has been paid to the failure mechanisms of Mg alloys, such as brittle fracture and fatigue, subjected to different environmental or loading conditions. In this work, tension, impact, bend and fatigue tests were conducted in an AM60 magnesium alloy.

Nanostructured high strength Mg-5%Al-x%Nd alloys prepared by mechanical alloying

Nanostructured high strength Mg-5%Al-x%Nd alloys were prepared by mechanical alloying. Microstructural characterization reveled average crystalline size to be about 30 nm after mechanical alloying while it increased to about 90 nm after sintering and extrusion. Mechanical properties showed increase in 0.2% yield stress, ultimate tensile strength was attributed to reduction in gain size as well as to the enhanced diffusion after mechanical activation. Although ultra high yield stress was observed from the specimen with 5% Nd, its ductility was reduced to about 1.6%.

Fabrication and microstructure of mechanically alloyed Mg-Al-Nd alloys

In this work, nanocrystalline Mg-Al-Nd alloys were fabricated using mechanical alloying method. Phase structure of the extrided rods was examined using X-ray diffraction (XRD) and the microstructures were observed using transmission electronic microscopy (TEM). High yield strength was obtained in the alloys with a high Nd content due to grain refinement and Nd rich precipitate phase.

Analysis of strain-rate dependent mechanical behavior of single chondrocyte : a finite element study

Various studies have been conducted to investigate the effects of impact loading on cartilage damage and chondrocyte death. These have shown that the rate and magnitude of the applied strain significantly influence chondrocyte death, and that cell death occurred mostly in the superficial zone of cartilage suggesting the need to further understand the fundamental mechanisms underlying the chondrocytes death induced at certain levels of strain-rate. To date there is no comprehensive study providing insight on this phenomenon. The aim of this study is to examine the strain-rate dependent behavior of a single chondrocyte using a computational approach based on Finite Element Method (FEM). An FEM model was developed using various mechanical models, which were Standard Neo-Hookean Solid (SnHS), porohyperelastic (PHE) and poroviscohyperelastic (PVHE) to simulate Atomic Force Microscopy (AFM) experiments of chondrocyte. The PVHE showed, it can capture both relaxation and loading rate dependent behaviors of chondrocytes, accurately compared to other models.

Exploration of mechanisms underlying the strain-rate-dependent mechanical property of single chondrocytes

Based on the characterization by Atomic Force Microscopy (AFM), we report that the mechanical property of single chondrocytes has dependency on the strain-rates. By comparing the mechanical deformation responses and the Young’s moduli of living and fixed chondrocytes at four different strain-rates, we explore the deformation mechanisms underlying this dependency property. We found that the strain-rate-dependent mechanical property of living cells is governed by both of the cellular cytoskeleton (CSK) and the intracellular fluid when the fixed chondrocytes is mainly governed by their intracellular fluid which is called the consolidation-dependent deformation behavior. Finally, we report that the porohyperelastic (PHE) constitutive material model which can capture the consolidation-dependent behavior of both living and fixed chondrocytes is a potential candidature to study living cell biomechanics.

Similarity solutions for flow and heat transfer of non-Newtonian fluid over a stretching surface

Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

Impact and energy absorption of portable water-filled road safety barrier system fitted with foam

Portable water-filled barriers (PWFBs) are roadside appurtenances that are used to prevent errant vehicles from penetrating into temporary construction zones on roadways. A numerical model of the composite PWFB, consisting of a plastic shell, steel frame, water and foam was developed and validated against results from full scale experimental tests. This model can be extended to larger scale impact cases, specifically ones that include actual vehicle models. The cost-benefit of having a validated numerical model is significant and this allows the road barrier designer to conduct extensive tests via numerical simulations prior to standard impact tests Effects of foam cladding as additional energy absorption material in the PWFB was investigated. Different types of foam were treated and it was found that XPS foam was the most suitable foam type. Results from this study will aid PWFB designers in developing new generation of roadside structures which will provide enhanced road safety.

Effect of crack depth and specimen width on fracture toughness of a carbon steel in the ductile-brittle transition region

The effects of crack depth (a/W) and specimen width W on the fracture toughness and ductile±brittle transition have been investigated using three-point bend specimens. Finite element analysis is employed to obtain the stress-strain fields ahead of the crack tip. The results show that both normalized crack depth (a/W) and specimen width (W) affect the fracture toughness and ductile±brittle fracture transition. The measured crack tip opening displacement decreases and ductile±brittle transition occurs with increasing crack depth (a/W) from 0.1 to 0.2 and 0.3. At a fixed a/W (0.2 or 0.3), all specimens fail by cleavage prior to ductile tearing when specimen width W increases from 25 to 40 and 50 mm. The lower bound fracture toughness is not sensitive to crack depth and specimen width. Finite element analysis shows that the opening stress in the remaining ligament is elevated with increasing crack depth or specimen width due to the increase of in-plane constraint. The average local cleavage stress is dependent on both crack depth and specimen width but its lower bound value is not sensitive to constraint level. No fixed distance can be found from the cleavage initiation site to the crack tip and this distance increases gradually with decreasing inplane constraint.

Numerical investigation on stable crack growth in plane stress

Large deformation finite element analysis has been carried out to investigate the stress-strain fields ahead of a growing crack for compact tension .a=W D 0:5/ and three-point bend .a=W D 0:1 and 0:5/ specimens under plane stress condition. The crack growth is controlled by the experimental J -integral resistance curves measured by Sun et al. The results indicate that the distributions of opening stress, equivalent stress and equivalent strain ahead of a growing crack are not sensitive to specimen geometry. For both stationary and growing cracks, similar distributions of opening stress and triaxiality can be found along the ligament. During stable crack growth, the crack-tip opening displacement (CTOD) resistance curve and the cohesive fracture energy in the fracture process zone are independent of specimen geometry and may be suitable criteria for characterizing stable crack growth in plane stress.