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Summary Background Tuberculosis remains a global health challenge, with early diagnosis key to its reduction. Face-mask sampling detects exhaled Mycobacterium tuberculosis. We aimed to investigate bacillary output from patients with pulmonary tuberculosis and to assess the potential of face-mask sampling as a diagnostic method in active case-finding. Methods We did a 24-h longitudinal study in patients from three hospitals in Pretoria, South Africa, with microbiologically confirmed pulmonary tuberculosis. Patients underwent 1 h of face-mask sampling eight times over a 24-h period, with contemporaneous sputum sampling. M tuberculosis was detected by quantitative PCR. We also did an active case-finding pilot study in inhabitants of an informal settlement near Pretoria. We enrolled individuals with symptoms of tuberculosis on the WHO screening questionnaire. Participants provided sputum and face-mask samples that were tested with the molecular assay Xpert MTB/RIF Ultra. Sputum-negative and face-mask-positive individuals were followed up prospectively for 20 weeks by bronchoscopy, PET-CT, and further sputum analysis to validate the diagnosis. Findings Between Sept 22, 2015, and Dec 3, 2015, 78 patients with pulmonary tuberculosis were screened for the longitudinal study, of whom 24 completed the study (20 had HIV co-infection). M tuberculosis was detected in 166 (86%) of 192 face-mask samples and 38 (21%) of 184 assessable sputum samples obtained over a 24-h period. Exhaled M tuberculosis output showed no diurnal pattern and did not associate with cough frequency, sputum bacillary content, or chest radiographic disease severity. On May 16, 2018, 45 individuals were screened for the prospective active case-finding pilot study, of whom 20 had tuberculosis symptoms and were willing to take part. Eight participants were diagnosed prospectively with pulmonary tuberculosis, of whom six were exclusively face-mask positive at screening. Four of these participants (three of whom were HIV-positive) had normal findings on chest radiography but had treatment-responsive early tuberculosis-compatible lesions on PET-CT scans, with Xpert-positive sputum samples after 6 weeks. Interpretation Face-mask sampling offers a highly efficient and non-invasive method for detecting exhaled M tuberculosis, informing the presence of active infection both with greater consistency and at an earlier disease stage than with sputum samples. The approach shows potential for diagnosis and screening, particularly in difficult-to-reach communities. Funding Wellcome Trust, CARA (Council for At-Risk Academics), University of Leicester, the UK Medical Research Council, and the National Institute for Health Research. Video Abstract Download : Download video (47MB) Exhaled Mycobacterium tuberculosis output and detection of subclinical disease by face-mask sampling Dr Caroline Williams introduces the paper on exhaled Mycobacterium tuberculosis output and detection of subclinical disease by face-mask sampling YouTube link: https://youtu.be/G-8majbi2Y0

The underground high-voltage power transmission cables are high value engineering assets that suffer from multiple deteriorations through-out life cycles. Recent studies identified a new failure mode – the pitting corrosion deterioration on the layer of phosphor bronze reinforcing tape, which protects the oil-filled power transmission cables from oil leakage due to deterioration of the leads heath. Two models estimating the phosphor bronze tape life were established separately in this study. The first model, based on mathematical fitting, is generated using a replacement priority model from the power supply industry. This is considered as an empirical-based model. The second model, based on the corrosion fatigue mechanism, utilizes the information of the pit depth distribution and the concept of pit-to-crack transfer probability. The Bayesian inference approach is the conjunction algorithm to update the existing probability of failure (PoF) model with the newly identified failure modes. Through this algorithm, the integrated PoF model contains a more comprehensive background information while maintaining the empirical knowledge on the engineering assets’ performance.

Background Human to human transmission of SARS-CoV-2 is driven by the respiratory route but little is known about the pattern and quantity of virus output from exhaled breath. We have previously shown that face-mask sampling (FMS) can detect exhaled tubercle bacilli and have adapted its use to quantify exhaled SARS-CoV-2 RNA in patients admitted to hospital with Coronavirus Disease-2019 (COVID-19). Methods Between May and December 2020, we took two concomitant FMS and nasopharyngeal samples (NPS) over two days, starting within 24 hours of a routine virus positive NPS in patients hospitalised with COVID-19, at University Hospitals of Leicester NHS Trust, UK. Participants were asked to wear a modified duckbilled facemask for 30 minutes, followed by a nasopharyngeal swab. Demographic, clinical, and radiological data, as well as International Severe Acute Respiratory and emerging Infections Consortium (ISARIC) mortality and deterioration scores were obtained. Exposed masks were processed by removal, dissolution and analysis of sampling matrix strips fixed within the mask by RT-qPCR. Viral genome copy numbers were determined and results classified as Negative; Low: ≤999 copies; Medium: 1,000-99,999 copies and High ≥ 100,000 copies per strip for FMS or per 100µl for NPS. Results 102 FMS and NPS were collected from 66 routinely positive patients; median age: 61 (IQR 49 - 77), of which FMS was positive in 38% of individuals and concomitant NPS was positive in 50%. Positive FMS viral loads varied over five orders of magnitude (, Graphical abstract Image, graphical abstract

Novel sampling matrices were manufactured using 3D printing for the detection of respiratory pathogens in expired air. A specific configuration of the matrices was designed using Computer-Aided Design software. Polyvinyl alcohol (PVA) was printed using fused deposition modelling to create a multilayer matrix to enhance the capture of bacteria. The performance of these matrices was compared with gelatine filters that have been used for this work to date. PVA matrices (60 mm diameter) were contaminated with bacteria either by direct inoculation, or by aerosol exposure using an Omron A3 nebuliser. Rough and smooth morphotypes of Mycobacterium abscessus, M. smegmatis and M. bovis BCG, were used in this study to contaminate the matrices. PVA matrices and gelatine sampling filters were contaminated to compare recovery rates for quantitative analyses. These were dissolved in water, bacteria pelleted and DNA extracted followed by a Mycobacterium-specific quantitative Polymerase Chain Reaction (qPCR).The results showed that 3D printed PVA matrices are very effective to capture the bacteria. 3D printed PVA matrix and gelatine filters yielded results of the same order of magnitude for mycobacterial analyses, however, PVA matrix offers several advantages over the latter material. 3D printed PVA is considered as an economic and time-effective matrix as it is cheaper than gelatine filters. PVA is sufficiently robust to be handled and loaded into the surgical masks for sampling, compared to the brittle gelatine filters that required supportive frames. PVA is a synthetic material and it is suitable for DNA-based analyses, whilst gelatine is derived from animal collagen, and carries a high bacterial DNA background that interferes with the target DNA analysis. Furthermore, PVA dissolves in distilled water without requiring chemicals or enzymes, such as the case for gelatine hydrolysis. To summarise, 3D printed PVA sampling matrix is considered a promising tool used for microbiological diagnostic purposes.

This paper is an investigation on the failure mechanism involved in underground power transmission cables with their life limited by corrosion of phosphor bronze reinforcing tapes. In the present work, a detailed analysis of failed bronze tapes in an ammonium free environment has been undertaken and corrosion fatigue failure mechanism has been identified. A detailed examination of the tape samples is carried out using 2D and 3D optical microscopy and SEM. It follows a mechanical approach that confirms corrosion fatigue as the failure mechanism. SEM images reveal that the pits present on the surface could be the starting point for the crack that eventually leads to failure. Stress calculation shows that the tape could fail only if corrosion pits are present on the tape surface. Presence of corrosion pits, multi cracks and striations on the fractured surface demonstrates corrosion fatigue cracking as the failure mechanism across the tape samples.

In the sintering of ceramics, cracks are inevitably encountered after sintering. But very few studies have been presented in the literature for qualifying and quantifying effects of inhomogeneity on sintering kinetics. Therefore, a series of detailed sintering variables such as grain size, surface tension and diffusivity are chosen to study the effects of their inhomogeneity on sintering kinetics through a computational model calculated by computer.Furthermore, there are two main achievements in this computational model that first one is providing a numerical solution for the curvature at triple junction (pore tip) of microscopic particles, and second one is considering the effect of surface diffusion on first-stage sintering where diffusion mechanism is coupled by grain-boundary and surface diffusion.

For aliphatic polyesters such as PLAs and PGAs, there is a strong interplay between the hydrolytic degradation and erosion – degradation leads to a critically low molecular weight at which erosion starts. This paper considers the underlying physical and chemical processes of hydrolytic degradation and erosion. Several kinetic mechanisms are incorporated into a mathematical model in an attempt to explain different behaviours of mass loss observed in experiments. In the combined model, autocatalytic hydrolysis, oligomer production and their diffusion are considered together with surface and interior erosion using a set of differential equations and Monte Carlo technique. Oligomer and drug diffusion are modelled using Fick’s law with the diffusion coefficients dependent on porosity. The porosity is due to the formation of cavities which are a result of polymer erosion. The model can follow mass loss and drug release up to 100%, which cannot be explained using a simple reaction-diffusion. The model is applied to two case studies from the literature to demonstrate its validity. The case studies show that a critical molecular weight for the onset of polymer erosion and an incubation period for the polymer dissolution are two critical factors that need to be considered when predicting mass loss and drug release. Statement of Significance In order to design bioresorbable implants, it is important to have a mathematical model to predict polymer degradation and corresponding drug release. However, very different behaviours of polymer degradation have been observed and there is no single model that can capture all these behaviours. For the first time, the model presented in this paper is capable of capture all these observed behaviours by switching on and off different underlying mechanisms. Unlike the existing reaction-diffusion models, the model presented here can follow the degradation and drug release all the way to the full disappearance of an implant.

Phosphor bronze tape is a key protection component of underground power transmission cables. During the service life, it is affected by both corrosion and fatigue effects, leading to the failure of material and eventually the failure of cables. In the present work, the combined effect on the cable failure is studied in five stages: pit initiation, pitting corrosion control, pit-crack transfer, crack propagation control, and material failure. The cable time to failure is defined as the time needed for a corrosion pit on the tape surface to transfer into a crack resulting from a cyclic fatigue load condition. The pit-crack transfer is described statistically by a pitting corrosion to crack propagation transfer probability function. The result shows that a life prediction model can convey the long-term data of cables and can predict the years of failure. Subsequently, the life prediction model is extended and tested to include crack transfer probability function.

Phosphor bronze tapes used in underground power transmission cables are affected by pitting corrosion that can lead to cable failures. In the present work, the probability distribution of corrosion...

This paper presents a constitutive law that predicts the changes in elastic moduli, Poisson's ratio and ultimate tensile strength of bioresorbable polymers due to biodegradation. During biodegradation, long polymer chains are cleaved by hydrolysis reaction. For semi-crystalline polymers, the chain scissions also lead to crystallisation. Treating each scission as a cavity and each new crystal as a solid inclusion, a degrading semi-crystalline polymer can be modelled as a continuum solid containing randomly distributed cavities and crystal inclusions. The effective elastic properties of a degrading polymer are calculated using existing theories for such solid and the tensile strength of the degrading polymer is predicted using scaling relations that were developed for porous materials. The theoretical model for elastic properties and the scaling law for strength form a complete constitutive relation for the degrading polymers. It is shown that the constitutive law can capture the trend of the experimental data in the literature for a range of biodegradable polymers fairly well.

Finite element analysis is a powerful tool for the design of bioresorbable medical implants made of aliphatic polyesters such as bioresorbable vascular scaffolds. However polymer erosion has been traditionally modelled using empirical rules rather than differential equations. The rule-based models are difficult to implement in a finite element analysis. Consequently, these models have been limited to simple geometries such as plates or spheres. This paper presents a set of differential equations that govern the hydrolytic chain scission and bulk erosion of bioresorbable implants where polymer erosion is modelled using a differential equation instead of empirical rules. These differential equations can be conveniently solved using a commercial finite element package to calculate the molecular weight and mass loss as functions of time for bioresorbable implant made of aliphatic polyesters. A case study of Absorb bioresorbable vascular scaffolds (BVSs) is presented using data obtained from the literature, where 98 Absorb BVSs were implanted in 40 porcine coronary arteries. It is demonstrated that the finite element model can fit the data of both molecular weight and mass loss as functions of time to an accuracy of approximately 5%. The finite element model and the back-calculated model parameters can be used to design future implants that degrade in a controlled pattern with required mechanical performance.

Polyvinyl alcohol is used to 3D print (fused deposition modelling) sampling matrices for bacterial detection. A specific configuration was designed using Computer-Aided Design software. The mechanical properties of the printed samples were studied using uniaxial tensile testing, and compared to those of the original Polyvinyl alcohol filament, with and without heat treatment. The effects of different factors such as UV treatment, printing speed, infill density and printing direction on the mechanical properties of the printed samples including strength, strain and modulus of elasticity were studied. The results show that the effect of the fused deposition modelling process on the mechanical properties of the printed Polyvinyl alcohol cannot be explained by its exposure to heat. UV treatment reduced the strength, characteristic strains and Young's modulus. It makes Polyvinyl alcohol samples brittle. The effects of printing speed and the infill density on the mechanical properties of printed samples can be no linear. An unexpected relation between printing direction and mechanical properties was demonstrated by the studied specimens that needs further theoretical understanding. There is a huge scatter in strength of PVA samples compared with typical engineering materials, and in the fracture strain of original PVA filament, the 3D printing process can reduce the scatter but only by a limited extent. To summarise, there is a sophisticated relation between printing parameters and the mechanical properties of the printed Polyvinyl alcohol.

Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide).

This paper presents a computational study of the role played by surface diffusion on first-stage sintering of powders that densify by grain-boundary diffusion. Coupled grain-boundary and surface diffusion is considered as the mechanism for matter redistribution. By using several novel approaches of presentation of the numerical data, it is shown that the assumption of fast surface diffusion is invalid for typical sintering conditions and materials in first stage of sintering. The study reveals a simple explanation for the role played by surface diffusion in matter redistribution of combined grain-boundary and surface diffusion—surface diffusion changes direction from moving atoms away from a contact neck to depositing atoms onto it as the rate of surface diffusion increases. The reverse surface diffusion blunts the neck and retards densification. It is shown that this mechanism is significant not only for free sintering but also for pressure assisted sintering. It is further confirmed that the widely observed beneficial effect of spark plasma sintering on densification can be, at least partially, attributed to its fast heating rate, which quickly passes through sintering at low temperatures where surface diffusion dominates.

A mathematical model was developed to relate the degradation trend of bioresorbable polymers to different underlying hydrolysis mechanisms, including noncatalytic random scission, autocatalytic random scission, noncatalytic end scission or autocatalytic end scission. The effect of each mechanism on molecular weight degradation and potential mass loss was analysed. A simple scheme was developed to identify the most likely hydrolysis mechanism based on experimental data. The scheme was first demonstrated using case studies, then used to evaluate data collected from 31 publications in the literature to identify the dominant hydrolysis mechanisms for typical biodegradable polymers. The analysis showed that most of the experimental data indicates autocatalytic hydrolysis, as expected. However, the study shows that the existing understanding on whether random or end scission controls degradation is inappropriate. It was revealed that pure end scission cannot explain the observed trend in molecular weight reduction because end scission would be too slow to reduce the average molecular weight. On the other hand, pure random scission cannot explain the observed trend in mass loss because too few oligomers would be available to diffuse out of a device. It is concluded that the chain ends are more susceptible to cleavage, which produces most of the oligomers leading to mass loss. However, it is random scission that dominates the reduction in molecular weight.

a b s t r a c t Introduction: The strengthening effect of prophylactic internal fixation (PIF) with a bone plate at the radial osteocutaneous flap donor site has previously been demonstrated using the sheep tibia model of the human radius. This study investigated whether a finite element (FE) model could accurately represent this biomechanical model and whether stress or strain based failure criteria are most appropriate. Methods: An FE model of an osteotomised sheep tibia bone was strengthened using 4 types of plates with unilocking or bicortical screw fixation. Torsion and 4-point bending simulations were performed. The maximum von Mises stresses and strain failure criteria were studied. Results: The strengthening effects when applying stress failure criteria (factor 1.76-4.57 bending and 1.33-1.80 torsion) were comparable to the sheep biomechanical model (factor 1.73-2.43 bending and 1.54-2.63 torsion). The strongest construct was the straight 3.5 mm stainless steel unilocking plate. Applying strain criteria the strongest construct was the straight 3.5 mm stainless DCP plate with bicortical screw fixation. Conclusions: The FE model was validated by comparison with the sheep tibia model. The complex biome- chanics at the bone-screw interface require further investigation. This FE modelling technique may be applied to a model of the human radius and other sites.

A numerical method to predict the break force of curved faced tablets is proposed. The constitutive model and the failure criteria necessary to obtain predictions consistent with experimental data are identified. A modified Drucker-Prager cap model together with a maximum principal stress based failure criteria was found sufficient to predict the break force of tablets under diametrical compression loading. The conditions for the validity of the method were identified with reference to practical tablet shapes and failure patterns. Under these conditions the numerical procedures can be used as a practical tool to predict tablet breakage as an alternative to the empirical methods currently used in pharmaceutical product design and process development.

In this paper we examine how the operation of an interface reaction influences the response of a body which deforms as the result of the transportation of material around the grains by grain-boundary diffusion. A characteristic material length scale λ is identified. If λ is much less than a suitably chosen physical length scale for a problem then the rate of diffusion controls the overall rate of the process. If, however, λ is comparable with the physical length scale then the interface reaction dominates the response. A range of problems are examined which provide a number of different possible physical length scale.

Sintering of ceramic films on a solid substrate is an important technology for fabricating a range of products, including solid oxide fuel cells, micro-electronic PZT films and protective coatings. There is clear evidence that the constrained sintering process is anisotropic in nature. This paper presents a study of the constrained sintering deformation using an anisotropic constitutive law. The state of the material is described using the sintering strains rather than the relative density. In the limiting case of free sintering, the constitutive law reduces to a conventional isotropic constitutive law. The anisotropic constitutive law is used to calculate sintering deformation of a constrained film bonded to a rigid substrate and the compressive stress required in a sinter-forging experiment to achieve zero lateral shrinkage. The results are compared with experimental data in the literature. It is shown that the anisotropic constitutive law can capture the behaviour of the materials observed in the sintering experiments.

The continuity conditions across a junction between a grain-boundary and a free surface are discussed for the coupled surface and grain-boundary diffusion problem. An appropriate treatment of the continuity is proposed, which forms the basis of a numerical procedure for an arbitrary network of grains containing pores of arbitrary shape and size. The analysis technique, when combined with a suitable time integration algorithm, is able to simulate physical processes such as powder sintering, diffusional void growth and creep crack propagation etc. which are dominated by the coupled diffusion mechanism under many practical circumstances. Currently only two-dimensional problems are discussed. The basic principles proposed in this paper, however, are also valid for three-dimensional situations. Simple numerical examples of powder sintering are given while the full potential of the numerical technique for the above physical problems will be exploited in a forthcoming paper.

This paper presents a numerical study on using vibration analysis to detect degradation in degrading polyesters. A numerical model of a degrading plate sample is considered. The plate is assumed to degrade following the typical behaviour of amorphous copolymers of polylactide and polyglycolide. Due to the well-known autocatalytic effect in the degradation of these polyesters, the inner core of the plate degrades faster than outer surface region, forming layers of materials with varying Young׳s modulus. Firstly the change in molecular weight and corresponding change in Young׳s modulus at different times are calculated using the mathematical models developed in our previous work. Secondly the first four mode shapes of transverse vibration of the plate are calculated using the finite element method. Finally the curvature of the mode shapes are calculated and related to the spatial distribution of the polymer degradation. It is shown that the curvature of the mode shapes can be used to detect the onset and distribution of polymer degradation. The level of measurement accuracy required in an experiment is presented to guide practical applications of the method. At the end of this paper a demonstration case of coronary stent is presented showing how the method can be used to detect degradation in an implant of sophisticated structure.

Cracking is a major problem during constrained sintering of ceramic films. A local variation of density in a green film, referred to as a defect in this work, is the leading cause for cracking. This article presents analytical and numerical studies of the behavior of such defects during constrained sintering. An interesting behavior of de-sintering and healing of the defects is revealed. It is demonstrated that the healing process can be made to start earlier during sintering by using (a) larger particles, (b) lower sintering temperature, and (c) lower initial density. However, a uniform distribution of initial density in the film is shown to be the most effective means to avoid cracking. It is realized that most of the factors beneficial to defect healing are detrimental to sintering a film to high density because the driving force for sintering also drives cracking. The analytical and numerical studies also offer some simple explanations to why thin films are less susceptible to cracking than thick ones. Finally, the constitutive model has been combined with a simple empirical failure criterion, to simulate the initiation and propagation of multiple cracks in a sintering film. The cracking patterns predicted by the simulations resemble those observed during sintering experiments.

This paper presents a molecular dynamics study on the change in Young’s modulus of semi-crystalline polymers during degradation by chain scissions, which is relevant to the study of mechanical properties of biodegrading polymers. Using a simple polymer model whose structural and mechanical properties are similar to that of a commonly used biodegrading polymer poly(glycolic acid), we combine molecular dynamics and Monte Carlo to model a system of two polymer crystals separated by an amorphous region between them. The polymer chains in the amorphous region are cut randomly to mimic hydrolysis chain scissions. In a series of virtual tensile tests, the systems with various numbers of chain scissions are subjected to a unidirectional deformation. We find that at temperatures below the glass transition temperature of the model polymer, the Young’s modulus of the system reduces quickly with the number of chain scissions, while at temperatures above the glass transition temperature, the Young’s modulus reduction lags behind the polymer chain scissions. This observation supports the entropy-spring model of amorphous polymers proposed by Wang et al., which suggests that Young’s modulus above the glass transition temperature is dominated by the internal energy of the system, while below the glass transition temperature it is dominated by the entropy of the amorphous phase. The numerical study therefore provides a molecular understanding of the widely observed behaviours of semi-crystalline biodegradable polymers.

Calibration procedures for constitutive models for powder compaction are presented. A practical calibration method based on a die compaction experiment is presented. A newly developed apparatus consisting of a die instrumented with radial stress sensors is described. The paper proposes two contributions to account for errors present in instrumented die testing, which are due to 1) elastic compliance of the testing frame, influencing the measurement of axial strain and 2) the presence on non-homogeneous stress state in the test specimen. It is shown that system compliance is important for generating an accurate stress-strain curve for compression. The effect of different compliance correction methods is evaluated with regard to the accuracy of models predicting pressing forces. The system compliance becomes more significant during unloading in the die; this information is used to determine the elastic properties. A new compliance correction method is introduced following a detailed analysis of the forces and deformations of different parts of the loading frame. In instrumented die compaction the axial and radial stresses are measured at fixed locations and the specimen is subject to non-homogeneous stresses and strains due to the effect of friction between the powder and die wall. Starting from the Janssen-Walker method of differential slices a method to account for non-homogeneous stress and strain is developed.

Understanding the impact failure of particles made of brittle materials such as glasses, ceramics and rocks is an important issue for many engineering applications. During the impact, a solid particle is turned into a discrete assembly of many fragments through the development of multiple cracks. The finite element method is fundamentally ill-equipped to model this transition. Recently a so-called material point method (MPM) has been used to study a wide range of problems of material and structural failures. In this paper we propose a new material point model for the brittle failure which incorporates a statistical failure criterion. The capability of the method for modelling multiple cracks is demonstrated using disc particles. Three impact failure patterns observed experimentally are captured by the model: Hertzian ring cracks, meridian cracks, and multi-fragment cracks. Detailed stress analysis is carried out to interpret the experimental observations. In particular it is shown that the experimentally observed dependence of a threshold velocity for the initiation of meridian cracks on the particle size can be explained by the proposed model. The material point based scheme requires a relatively modest programming effort and avoids node splitting which makes it very attractive over the traditional finite element method.

This paper presents a numerical study on contact law between extremely fine particles taking into account of the effect of adhesion force and surface roughness. The adhesion force between two particles is calculated from the Erkoc inter-atomic potential. This force is incorporated into a material point model for the dynamic impact between the two particles. Unlike a molecular dynamics model, atoms in the model are embedded in the continuum solid such that they can only move relatively to each other as the continuum solid deforms. The model is numerically efficient while taking into account of the adhesion effect at the same time . Numerical study using this model shows that the Maugis theory ( Maugis, 1992 ) is valid for spherical particles as small as 50 nm in size. The numerical study also shows that a slight change in surface roughness can alter the impact behaviour completely. Therefore an uncertainty in using the Maugis contact law for real particles is how to determine the effective specific surface energy for particles of different surface roughness. Because of the uncertainty, full numerical analysis may have to be used to obtain the adhesive contact law.

This paper presents a computer model for the biodegradation of polyesters such as poly(lactic acid), poly(glycolic acid) and their copolymers. The model can take polymer details such as molecular weight distribution, different end and random scission rates and copolymer ratio as input data. A multi-scale approach is developed: polymer chain scission and oligomer production which occur at the molecular scale are modelled using a kinetic Monte Carlo scheme, oligomer diffusion which occurs at the device scale is modelled using a diffusion equation, and the two are connected at the finite difference nodes of the diffusion equation. The two-scale model can be used to predict the temporal evolution and spatial distribution of molecular weight distribution in a device as well as the weight loss as a function of time. It is shown that the kinetic Monte Carlo scheme can accurately predict the effect of copolymer ratio on the degradation rate. Grizzi and co-workers observed in their experiments that a PLA film 0.3mm thick degrades much more slowly than one that is 2mm thick. The numerical study shows that the conceptional reaction diffusion model suggested by Grizzi et al. needs to be extended in order to explain the size effect fully.

Die compaction of powders is a process which involves filling a die with powder, compaction using rigid punches to form a dense compact and ejection from the die. The process can be treated as a large deformation plasticity problem. The challenge is to develop and implement appropriate constitutive models that capture the evolution of the powder from a loose state into a dense compact. In this paper we describe data analysis procedures and calibrate classic incremental plasticity models, such as Cam-Clay, Drucker-Prager cap models. The complexity of the models is increased from models with a hardening law to more complex constitutive models using density as state variable. The compaction behaviour of a range of powder materials is characterized experimentally. Numerical simulation of the compaction of simple parts and complex parts is demonstrated. The merits of various models are evaluated in terms of the balance between complexity and practicality. The discussion is illustrated with case studies exploring the applicability of the models specific to various powder pressing scenarios.

The degradation of medical devices made of bioresorbable polymers such as fixation devices in orthopaedic surgeries and scaffolds for tissue engineering can take from months to years. The trial and error approach of device development is therefore problematic and mathematical modelling of the biodegradation can help to accelerate the device development. This paper presents an inverse scheme to obtain the material parameters in a biodegradation model developed by Pan and his co-workers from existing experimental data of bioresorbable devices. The parameters can then be used to predict the degradation rate of new devices made of the same polymer. Firstly, the previously developed model is briefly outlined. Secondly, a finite element scheme and a time integration algorithm are developed for the direct analysis using the biodegradation model. Thirdly, an inverse analysis scheme is presented in combination with the direct analysis. Finally, several case studies of existing degradation data are presented to demonstrate the effectiveness of the inverse engineering approach.

This paper presents a model for the change in Young’s modulus of biodegradable polymers due to hydrolysis cleavage of the polymer chains. The model is based on the entropy spring theory for amorphous polymers. It is assumed that isolated polymer chain cleavage and very short polymer chains do not affect the entropy change in a linear biodegradable polymer during its deformation. It is then possible to relate the Young’s modulus to the average molecular weight in a computer simulated hydrolysis process of polymer chain sessions. The experimental data obtained by Tsuji [Tsuji, H., 2002. Autocatalytic hydrolysis of amorphous-made polylactides: Effects of L-lactide content, tacticity, and enantiomeric polymer blending. Polymers 43, 1789–1796] for poly(L-lactic acid) and poly(D-lactic acid) are examined using the model. It is shown that the model can provide a common thread through Tsuji’s experimental data. A further numerical case study demonstrates that the Young’s modulus obtained using very thin samples, such as those obtained by Tsuji, cannot be directly used to calculate the load carried by a device made of the same polymer but of various thicknesses. This is because the Young’s modulus varies significantly in a biodegradable device due to the heterogeneous nature of the hydrolysis reaction. The governing equations for biodegradation and the relation between the Young’s modulus and average molecular weight can be combined to calculate the load transfer from a degrading device to a healing bone.

This paper presents a comprehensive study for the contact laws between solid particles taking into account the effects of plasticity, strain hardening and very large deformation. The study takes advantage of the development of a so-called material point method (MPM) which requires neither remeshing for large deformation problems, nor iterative schemes to satisfy the contact boundary conditions. The numerical results show that the contact law is sensitive to impact velocity and material properties. The contact laws currently used in the discrete element simulations often ignore these factors and are therefore over-simplistic. For spherical particles made of elastic perfectly plastic material, the study shows that the contact law can be fully determined by knowing the relative impact velocity and the ratio between the effective elastic modulus and yield stress. For particles with strain hardening, the study shows that it is difficult to develop an analytical contact law. The same difficulty exists when dealing with particles of irregular shapes or made of heterogeneous materials. The problem can be overcome by using numerical contact laws which can be easily obtained using the material point method.

A classical sintering theory predicts that a pore with high coordination number grows instead of shrinking during sintering. This has led to the proposition that grain growth may be beneficial to densification. Pan and colleagues argue against this theory using computer simulations, while Flinn and colleagues have provided direct experimental evidence showing that very large pores shrink despite their high coordination number. The current paper brings the analytical and experimental work together. In particular, further computer simulation evidence is provided to support the argument and an analytical model is developed to predict the densification rate of powder compacts containing large and small pores. The analytical model shows that there is a sudden reduction in the shrinking rate of the large pores when the small pores are eliminated.

The paper presents a molecular dynamics study on the interactions between nanoparticles at elevated temperatures. The emphasis is on the comparison between the molecular dynamics model and the continuum model using solid state physics. It is shown that the continuum model is unable to capture the sintering behaviour of nanoparticles. This is not because the continuum theory does not apply at the nano-scale but because the nanoparticles behave in so many different scenarios of the continuum theory that a meaningful model has to predict these scenarios, using the molecular dynamics for example. In the MD simulation, it is observed that the particles reorient their crystalline orientations at the beginning of the sintering and form different types of “necks” between different particles. This leads to different mechanisms of matter redistribution at the different necks. It is also observed that the particles can switch the mechanism of matter transportation half-way through the sintering process. It would be very difficult, if not impossible, to handle these complexities using the continuum model. However assuming the right scenario, the continuum theory does agree with the MD simulation for particles consisting of just a few thousands atoms.

Predicting the sintering deformation of ceramic powder compacts is very important to manufactures of ceramic components. In theory the finite element method can be used to calculate the sintering deformation. In practice the method has not been used very often by the industry for a very simple reason – it is more expensive to obtain the material data required in a finite element analysis than it is to develop a product through trial and error. A finite element analysis of sintering deformation requires the shear and bulk viscosities of the powder compact. The viscosities are strong functions of temperature, density and grain-size, all of which change dramatically in the sintering process. There are two ways to establish the dependence of the viscosities on the microstructure: (a) by using a material model and (b) by fitting the experimental data. The materials models differ from each other widely and it can be difficult to know which one to use. On the other hand, obtaining fitting functions is very time consuming. To overcome this difficulty, Pan and his co-workers developed a reduced finite element method (Kiani et. al. J. Eur. Ceram. Soc., 2007, 27, 2377-2383; Huang and Pan, J. Eur. Ceram. Soc., available on line, 2008) which does not require the viscosities; rather the densification data (density as function of time) is used to predict sintering deformation. This paper provides an overview of the reduced method and a series of case studies.

This paper presents a phenomenological diffusion-reaction model for the biodegradation of biodegradable polymers. The biodegradation process is modelled using a set of simplified reaction-diffusion equations. These partial differential equations are non-dimensionalised giving two normalised parameters which control the interplay between the hydrolysis reaction and the monomer diffusion. The equations are firstly solved for simple cases of plates and pins. The numerical results are presented in the form of biodegradation maps which show the conditions where the biodegradation is controlled by auto-catalysed hydrolysis, non-catalysed hydrolysis, a combination of auto-catalysed and non-catalysed hydrolyses, or a combination of hydrolysis and monomer diffusion, respectively. The degradation maps provide a clear guide for the design of biodegradable fixation devices used in orthopaedic surgeries. Finally the diffusion-reaction equations are solved using the finite element method for strip and square meshes, showing how the model can be used to assist the design of sophisticated fixation devices.

Bioglass-based glass-ceramic foams have been developed recently as highly porous, mechanically competent, bioactive and degradable scaffolds for bone tissue engineering. However, the development of the material so far has been based on a trial-and-error approach, and the existing materials are far from being optimized. In this paper, a mechanism-based model is presented for sintering deformation of Bioglass foams. The porous foams consist of struts which, in turn, consist of Bioglass particles. A corresponding two-scale model is developed based on existing viscous sintering models. Crystallization plays a key role in the sintering deformation of Bioglass foams and is taken into account in the model. Qualitative comparison between the model predictions and experimental observations is presented, showing that the model is able to capture the complicated interplay between crystallization and viscous flow during the sintering process.

In a previous paper, Kiani et al. [Kiani, S., Pan, J., Yeomans, J. A., Barriere, M. B. and Blanchart, P., Finite element analysis of sintering deformation using densification data instead of a constitutive law. J. Eur. Ceram. Soc., 2007, 27 , 2377–2383] proposed an empirical numerical method to calculate the sintering deformation of ceramic powder compacts without knowing the viscosities and sintering potential. The method was validated by free sintering experiments using specimens with non-uniform initial densities. Two new developments are reported in this paper: (a) a method of error estimation is developed which can be used to check if the empirical analysis is valid after the analysis; (b) a range of case studies are presented showing that the empirical solutions provide very good approximations to the solutions obtained using full constitutive laws not only for free sintering but also for highly constrained sintering of single- or multi-layered films.

This paper presents a numerical model for the early stage sintering of powder compact taking into account of the separation of contact necks. The neck separation or damage may occur in a powder matrix which contains large second phase inclusions. A damage parameter is introduced and a variational principle for the sintering deformation of the matrix is developed using the damage parameter as a control variable. The sintering problem is therefore modelled by the minimisation of a quadratic functional under the control of a Kuhn–Tucker condition of damage growth. A sequential quadratic programming algorithm is used to solve the minimisation problem, giving temporal evolution of the stresses, strains, damage parameter and deformation of the matrix material. A range of numerical examples are given and the results are qualitatively compared with experimental observations made by Sudre et al. [Sudre, O., Bao, G., Fan, B., Lange, F.F., Evans, A.G., 1992. Effects of inclusions on densification. II: Numerical model. Journal of the American Ceramic Society 75, 525–531] and by Lange [Lange, F.F., 1989. Densification of powder ring constrained by dense cylindrical core. Acta Metallurgica 37, 697–704].

A computer simulation study of the sintering process of cylindrical particles is presented following an earlier work by Pan et al. [Pan J, Le H, Kucherenko S, Yeomans JA. A model for the sintering of spherical particles of different sizes by solid state diffusion. Acta Metall 1998;46:4671–90]. The current paper focuses on the effect that the size of the particles has on the sintering kinetics. The computer simulation revealed a sophisticated behaviour for this apparently well-understood problem. Firstly, it is shown that a smaller particle can grow temporarily at the expense of its larger neighbours, in contradiction to conventional wisdom. There are two conditions for this to happen: (a) the particles must be nano-sized and (b) the smaller particle must be placed between two larger neighbours. Secondly, a pair of nanoparticles of different size can separate from each other in the later stage of their co-sintering process. Thirdly, the extent to which particles approach each other is strongly influenced by degree of constraint that the particles are subjected to by the neighbouring particles. This sophisticated behaviour revealed by the computer simulation questions the relevance of the oversimplistic sintering models to a real powder compact.

Various forms of constitutive laws have been developed for use in the finite element analysis of sintering deformation. Some of these were based on micromechanical models and others were based on empirical fitting of experimental data. The mechanism-based constitutive laws differ from each other widely and it can be difficult to know which one to use. On the other hand, obtaining fitting functions for an empirical constitutive law is very time consuming. In this paper, an empirical finite element method is presented which does not require a constitutive law; rather the densification data (density as a function of time) is used to predict sintering deformation. The densification data can be obtained by sintering a relatively small number of samples of the powder or derived from the master sintering curve. Different sintering mechanisms and non-linearity pose no difficulty to the method. The method is, however, limited to pressureless sintering. To verify the densification-based finite element method, three case studies are presented. The numerical predictions were compared with experimental measurement for two different cases. It is shown that the accuracy of the prediction is well within the experimental uncertainties and comparable to previous finite element analyses using full constitutive laws.

The master sintering curve approach represents densification data in terms of a master variable that combines sintering time and temperature. Recently, a finite-element scheme to predict sintering deformation that requires only the master sintering curve instead of a full constitutive law as the input data has been developed. Here, a modification to the original master sintering curve approach, so that it is more suitable for finite-element analysis, is presented. Finite-element shape functions are used to represent the densification data as well as the master sintering curve. This approach confers extra flexibility to the master sintering curve approach, even when it is not used with finite-element analysis. For example, by using shape functions, a varying activation energy can be used to obtain a master sintering curve for a set of densification data that cannot be fitted using a constant activation energy.

The sintering kinetics of large pores in a dense polycrystalline solid is studied using computer simulation. Coupled grain-boundary diffusion, surface diffusion and grain-boundary migration are assumed as the underlying mechanisms for the microstructural evolution. A numerical method developed by Ch’ng and Pan [Ch’ng, H.N., Pan, J., 2004. Cubic spline elements for modelling microstructural evolution of materials controlled by solid state diffusion and grain-boundary migration. Journal of Computational Physics 196, 724], which is an improved version of that developed by Pan et al. [Pan, J., Cocks, A.C.F., Kucherenko, S., 1997. Finite element formulation of coupled grain-boundary and surface diffusion with grain-boundary migration. Proceedings of the Royal Society, London A 453, 2161], is used for the computer simulation. A well-known textbook theory due to Kingery and Francois [Kingery, W.D., Francois, B., 1967. The sintering of crystalline oxides. I. Interaction between grain boundaries and pores. In: Kuczynski, G.C., et al. (Eds.), Sintering Related Phenomena. Goedon and Breach, New York, p. 471] predicts that a critical coordination number exists above which a pore does not shrink. The computer simulation demonstrates that this is not a general rule and that the critical coordination number only exists if one assumes that the pore is surrounded by identical grains. This numerical finding explains the contradiction between existing experimental observations and the critical coordination number theory. The numerical results also support the analytical expression developed by Ma [Ma, J., 1997. Constitutive modelling of the densification of porous ceramic components. PhD thesis, Engineering Department, Cambridge University] and Cocks [Cocks, A.C.F., 2001. Constitutive modelling of powder compaction and sintering. Progress in Materials Science 46, 201] for the sintering potential of powder containing large pores.

This paper presents a numerical scheme for computer simulation of microstructural evolution of porous polycrystalline materials at elevated temperatures. The scheme is then applied to study the sintering behaviour of polycrystalline solid containing elongate pores. In a previous paper [J. Comput. Phys. 196 (2004) 724], we presented a set of finite element formulations to model surface diffusion, grain-boundary diffusion and grain-boundary migration, and their interactions. A range of numerical examples were provided for which analytical solutions are available to verify the finite element formulations. All these examples had to be simple and contained at most two grains for the analytical solutions to be possible. In this paper, we complete the numerical scheme and address the numerical issues which have to be resolved when applying the finite element formulations to material models consisted of many grains and pores. In particular, we demonstrate how the joining conditions at triple junctions are achieved in the finite element solution and how the microstructure is updated according to the velocities obtained from the finite element solution. The numerical scheme is then used to study the problem of anisotropic sintering. A series of computer simulations were carried out to study microstructural evolution around an elongate pore. The numerical results show that an elongate pore leads to anisotropic shrinkage and that the shrinkage is always larger in the direction of the longer axis of the pore. The numerical results also show that the shrinkage anisotropy can be controlled by manipulating the ratios between the kinetic mobilities of surface diffusion, grain-boundary diffusion and grain-boundary migration. Increasing the grain-boundary migration mobility increases the shrinkage anisotropy. Increasing the surface diffusion mobility, on the other hand, reduces the shrinkage anisotropy. These numerical findings are not obvious and remain to be verified by future experiment.

This paper presents a model for the evolution of creep damage by the nucleation, growth and coalescence of multiple cavities at a grain-boundary. Coupled grain-boundary and surface diffusion is assumed as the mechanism of cavity growth. At the core of the model is a simplified finite element formulation of cavity growth. Each cavity is modelled using a cavity element, these can be assembled together to construct a grain-boundary network with an evolving distribution of cavities. The cavity element is an extension of our previous model for the growth of a single cavity (Westwood et al., 2000). Continuous nucleation and coalescence of cavities are integrated into the model through remeshing the grain-boundary at a nucleation or coalescence event. The finite element formulation is tested using a series of cases for which the solutions are known. The finite element model is then compared with the smeared out model which was first proposed by Tvergaard (1983) and later adopted by Onck and van der Giessen (1997, 1999). It is shown that the two models only agree with each other at either a unrealistically high level of applied stress or extremely low rate of the nucleation. Under realistic values of applied stress and relative diffusivity, the smeared-out model tends to over-predict the damage growth rate. Finally the effect of relative diffusivity on creep damage is investigated. It is confirmed that materials with fast surface diffusivity possess a high resistance to diffusional damage growth, but this effect is only significant at a relatively high level of applied stress.

A nonlinear kinetic law and its corresponding variational principle are developed for solid-state diffusion under a large thermodynamic driving force. These are used to model the sintering of spherical particles. It is demonstrated that the classical linear diffusion law significantly underpredicts the sintering rate for nanosized particles.

A new set of finite element formulations are presented in this paper to model surface diffusion, grain-boundary diffusion, grain-boundary migration and their interaction. The new formulations use the classical cubic splines both to represent material interface and to act as shape functions for the migration velocity of the interface. The smoothness of the interface is enforced such that the second order derivatives of the migration velocity is continuous anywhere on the interface. This is achieved by using the cubic spline shape functions and by introducing two new Lagrange terms in the variational principle. The work presented here is a new development to the finite element scheme which was previously developed by Pan, Cocks and their co-workers [Comput. Mater. Sci. 18 (2000) 76: Comput. Mater. Sci. 1 (1993) 95; Acta Mater. 43 (1995) 1395: Proc. Roy. Soc. London A 453 (1997) 2161] for modelling microstructural evolution of materials. The cubic spline elements provide a numerically efficient alternative to the linear elements used by Pan et al. [Proc. Roy. Soc. London A 453 (1997) 2161]. The finite element formulations are verified using a series of test cases for which analytical solutions exist in the literature. A further demonstration case of the co-sintering of two particles of different sizes is provided. The new finite element scheme has made it possible to carry out computer simulations of microstructural evolution using sophisticated and more realistic material models than ever before. The over-simplifications in various existing material models can lead to incorrect predictions. This is dramatically demonstrated in a separate paper in which the finite element scheme is used to investigate the sintering behaviour of large pores [Mech. Mater. (2003)].

This paper presents a numerical scheme for solving the governing equations of the phase field model for microstructural evolution of materials. Grain-growth is used as an example but the scheme can be applied to any general phase field model. The numerical scheme is a Galerkin scheme using Daubechies wavelets as the trial and weight functions. Multi-level Daubechies wavelets with six vanishing moments are used. Using the wavelets as the trial and weight functions has the advantage of focusing the numerical calculation to where the field variable has high gradient, i.e. the interfacial boundaries. The numerical scheme therefore overcomes the problem of computational inefficiency in the phase field models. In this paper we first explain the wavelet-Galerkin scheme using a one-dimensional example for its simplicity and then extend the scheme to three-dimensional problems. By comparing the wavelet-Galerkin scheme with a classical finite difference scheme for both one and three-dimensional problems, the wavelet-Galerkin scheme is verified and its computational efficiency is demonstrated especially for three-dimensional problems.

Recent developments in modelling the sintering process of powder compacts are critically reviewed. Both free sintering and pressure assisted sintering are considered. The review approaches the sint...

This Chapter introduces a rate equation for polymer chain scission in which carboxylic end groups on long and short chains are partitioned. This partition is necessary because only the short chains can diffuse and the carboxylic end groups on long chains may be a poor catalysts for hydrolysis. Analytical solutions are provided for a range of cases. A parametric study is presented to demonstrate how the model parameters affect its behaviour. It is also demonstrated that end scissions are much faster than random scissions and responsible for weight loss while random scissions are responsible for reduction in the molecular weight.