Numerical investigation of the effect of porous titanium femoral prosthesis on bone remodeling

Porous titanium is a promising orthopedic implant material. As a potential use in total hip replacement, the effect of a porous titanium femoral prosthesis on bone remodeling is investigated in this paper. The stress and strain fields of a post-operative femur with a hip replacement are calculated by applying the three-dimensional finite element method. The effect of the implant material on the bone remodeling is evaluated by analyzing the loss of bone density following a strain magnitude based bone remodeling theory. Different implant materials, including currently used solid cobalt–chrome and solid titanium, potential porous titanium with different porosities, are considered in this study. This investigation confirms that bone loss around the implant strongly depends on the value of the elastic modulus of the prosthesis. There will be a sharp drop of the volume of the bone with density loss if a cobalt–chrome implant is replaced by a porous titanium implant. The numerical results show that both of the bone volume with density loss and the bone density loss rate decrease linearly with the increase of the porosity. However, increasing porosity will reduce the strength of porous titanium. With regard to material design for porous titanium-based femoral prosthesis, stress analysis is required to meet the strength requirement.     

Strong materials – a structural view of material strength down to a molecular scale: Concept of a novel strong and extremely light weight molecular space frame‐polymer

The paper presents the concept of a novel very low density polymer with a rather high stiffness and possibly a high strength. The polymer molecular structure is related to a macroscopic structural engineering principle, a static (over‐) determined space frame. Before describing the molecular space frame in detail, it is discussed how and when macroscopic mechanical principles can be applied to molecular structures. It will be made plausible that this can be done to a large extent. In that way a material with an extremely fine aerogel‐like structure can be created, showing a very low density and a high stiffness to density‐ratio.     

Generalized approach to estimation of strains and stresses at blunt V‐notches under non‐localized creep

Geometrical discontinuities such as notches need to be carefully analysed by engineers because of the stress concentration generated by them. Notches become even more important when the component is subjected, in service, to very severe conditions, such as high‐temperature fatigue and imposed viscoplastic behaviour such as creep. The knowledge of strains and stresses in such stress concentration zones is essential for an efficient and safe design process. The aim of the paper is to present an improvement and extension of the existing notch‐tip creep stress–strain analysis method developed by Nuñez and Glinka, validated for U‐notches only, to a wide variety of blunt V‐notches. The key in obtaining the extension to blunt V‐notches is the substitution of the Creager–Paris equations with the more generalized Lazzarin–Tovo solution, allowing a unified approach to the evaluation of linear elastic stress fields in the neighbourhood of both cracks and notches. Numerous examples have been analysed to date, and the stress fields obtained according to the proposed method were compared with appropriate finite element data, resulting in a very good agreement. In view of the promising results discussed in the paper, authors are considering possible further extension to sharp V‐notches and cracks introducing the concept of the strain energy density.     

Flexoelectricity in Bones

Bones generate electricity under pressure, and this electromechanical behavior is thought to be essential for bone's self‐repair and remodeling properties. The origin of this response is attributed to the piezoelectricity of collagen, which is the main structural protein of bones. In theory, however, any material can also generate voltages in response to strain gradients, thanks to the property known as flexoelectricity. In this work, the flexoelectricity of bone and pure bone mineral (hydroxyapatite) are measured and found to be of the same order of magnitude; the quantitative similarity suggests that hydroxyapatite flexoelectricity is the main source of bending‐induced polarization in cortical bone. In addition, the measured flexoelectric coefficients are used to calculate the (flexo)electric fields generated by cracks in bone mineral. The results indicate that crack‐generated flexoelectricity is theoretically large enough to induce osteocyte apoptosis and thus initiate the crack‐healing process, suggesting a central role of flexoelectricity in bone repair and remodeling.     

Strain‐induced crystallization in rubber: A new measurement technique

The crystallinity of stretched crystallizable rubbers is classically investigated using X‐ray diffraction. In this study, we propose a new method based on temperature measurement and quantitative calorimetry to determine rubber crystallinity during mechanical tests. For that purpose, heat power density are first determined from temperature variation measurements and the heat diffusion equation. The increase in temperature due to strain‐induced crystallization is then deduced from the heat power density by subtracting the part due to elastic couplings. The heat capacity, the density, and the enthalpy of fusion are finally used to calculate the crystallinity from the temperature variations due to strain‐induced crystallization. The characterization of the stress–strain relationship and the non‐entropic contributions to rubber elasticity is not required. This alternative crystallinity measurement method is therefore a user‐friendly measurement technique, which is well adapted in most of the mechanical tests carried out with conventional testing machines. It opens numerous perspectives in terms of high speed and full crystallinity field measurements.     

Free surface density and microdamage in the bone remodeling equation: Theoretical considerations

Bone is maintained through a coupled process of bone resorption and bone formation, in a continuous process called bone remodeling. An imbalance in this process caused by disease, abnormal mechanical demands, or fatigue may predispose bone to fracture injuries. The remodeling process is generally viewed as a material response to functional demands. Here, we propose a new set of constitutive equations for the bone remodeling process and contains the specific surface, instead of volume fraction, and the degree of microcracking in the constitutive equations. The rate of remodeling is related to mechanical stimuli, free surface density and a microcrack factor. In this approach, the effect of mechanical stimuli, rate of mechanical stimuli, and integration of mechanical stimuli on bone remodeling can be evaluated simultaneously in the remodeling equation. Specific examples are given for illustration of the model.     

Controlled Assembly of Highly Raman‐Enhancing Silver Nanocap Arrays Templated by Porous Anodic Alumina Membranes

A convenient nanoscale technique is reported for the fabrication of highly ordered hemispherical silver nanocap arrays templated by porous anodic alumina (PAA) membranes as robust and cost‐efficient surface‐enhanced Raman scattering (SERS) substrates. This geometry produces a high Raman signal due to its periodic hexagonal arrangements and control of the gap between the nanostructures in the sub‐10‐nm regime. The surface structure can be tuned further to optimize the enhancement factor according to optional PAA fabrication and silver deposition parameters. Finite‐difference time‐domain calculations indicate that the structure may possess excellent SERS characteristics due to the high density and abundance of hot spots.     

A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns

The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. Following our recent works on quasi‐static modeling of phase‐field‐type brittle fracture, we propose in this paper a computational framework for diffusive fracture for dynamic problems that allows the simulation of complex evolving crack topologies. It is based on the introduction of a local history field that contains a maximum reference energy obtained in the deformation history, which may be considered as a measure of the maximum tensile strain in the history. This local variable drives the evolution of the crack phase field. Its introduction provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of a very robust algorithmic treatment for elastodynamic problems of diffusive fracture. Here, we extend the recently proposed operator split scheme from quasi‐static to dynamic problems. In a typical time step, it successively updates the history field, the crack phase field, and finally the displacement field. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples, which show the evolution of complex crack patterns under dynamic loading. Copyright © 2012 John Wiley & Sons, Ltd.     

Description of fatigue damage in carbon black filled natural rubber

The present paper describes macroscopic fatigue damage in carbon black‐filled natural rubber (CB‐NR) under uniaxial loading conditions. Uniaxial tension‐compression, fully relaxing uniaxial tension and non‐relaxing uniaxial tension loading conditions were applied until sample failure. Results, summarized in a Haigh‐like diagram, show that only one type of fatigue damage is observed for uniaxial tension‐compression and fully relaxing uniaxial tension loading conditions, and that several different types of fatigue damage take place in non‐relaxing uniaxial tension loading conditions. The different damage types observed under non‐relaxing uniaxial tension, loading conditions are closely related to the improvement of rubber fatigue life. Therefore, as fatigue life improvement is classically supposed to be due to strain‐induced crystallization (SIC), a similar conclusion can be drawn for the occurrence of different types of fatigue damage.     

Digital image correlation measurement of near‐tip fatigue crack displacement fields: constant amplitude loading and load history effects

Recent work by de Matos and colleagues employed digital image correlation to measure near tip displacement fields for fatigue cracks in 6082 T6 aluminium alloy. The main focus of this work was to directly measure fatigue crack closure, but the measurements can also be used to examine conditions at and ahead of the crack tip. In this paper, the results are re‐analysed and compared to two crack‐tip deformation models. The first assumes simple elastic deformation (according the Westergaard solution). This allows the history of crack‐tip stress intensity to be examined. Reasonable agreement with the elastic model is obtained, although there is a residual stress intensity caused by the plastic wake, which gives rise to crack closure. The second model examined is a simple elastic–plastic assumption, proposed by Pommier and colleagues. This can be applied to constant amplitude loading, although the results obtained here are very similar to the elastic case. A slightly more complex load case (a single overload in an otherwise constant amplitude variation of load) gives a much more complicated crack‐tip history. Here, the importance of crack‐tip plastic displacement, represented by the second term in Pommier's model becomes much clearer. Load history effects are captured by the residual value of this term and its associated displacement fields as well as by stress intensity factor. The implications for further modelling and experimental work are discussed.     

Sharp V‐notches in viscoplastic solids: Strain energy rate density rule and fracture toughness

Different from Neuber's rule or Glinka's energy method which are always adopted to characterize the notch tip field under elastoplastic condition, in this paper, the strain energy rate density (SERD) rule is used for viscoplastic materials. In particular, based on the definition of generalized notch stress intensity factor (G‐NSIF) for sharp V‐notch in viscoplastic solids, the concept of SERD for sharp V‐notch in viscoplastic solids is presented. Subsequently, by taking as a starting point the SERD, the averaged strain energy density (SED) for sharp V‐notch in viscoplastic solids is derived with integration of time. The fracture toughness relation between sharp V‐notch specimens and crack specimen in viscoplastic materials is given based on the transformation of SERD. A numerical approach is presented to compute the SERD and SED based on finite element method. Some crucial comments on the G‐NSIF have been discussed. Some typical solutions for SERD and SED for sharp V‐notched specimens are investigated.     

Ultrahigh‐Energy Density Lithium‐Ion Cable Battery Based on the Carbon‐Nanotube Woven Macrofilms

Moore's law predicts the performance of integrated circuit doubles every two years, lasting for more than five decades. However, the improvements of the performance of energy density in batteries lag far behind that. In addition, the poor flexibility, insufficient‐energy density, and complexity of incorporation into wearable electronics remain considerable challenges for current battery technology. Herein, a lithium‐ion cable battery is invented, which is insensitive to deformation due to its use of carbon nanotube (CNT) woven macrofilms as the charge collectors. An ultrahigh‐tap density of 10 mg cm^?2 of the electrodes can be obtained, which leads to an extremely high‐energy density of 215 mWh cm^?3. The value is approximately seven times than that of the highest performance reported previously. In addition, the battery displays very stable rate performance and lower internal resistance than conventional lithium‐ion batteries using metal charge collectors. Moreover, it demonstrates excellent convenience for connecting electronics as a new strategy is applied, in which both electrodes can be integrated into one end by a CNT macrorope. Such an ultrahigh‐energy density lithium‐ion cable battery provides a feasible way to power wearable electronics with commercial viability.     

A stabilized conforming nodal integration for Galerkin mesh‐free methods

Domain integration by Gauss quadrature in the Galerkin mesh‐free methods adds considerable complexity to solution procedures. Direct nodal integration, on the other hand, leads to a numerical instability due to under integration and vanishing derivatives of shape functions at the nodes. A strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integration. For convergence, an integration constraint (IC) is introduced as a necessary condition for a linear exactness in the mesh‐free Galerkin approximation. The gradient matrix of strain smoothing is shown to satisfy IC using a divergence theorem. No numerical control parameter is involved in the proposed strain smoothing stabilization. The numerical results show that the accuracy and convergent rates in the mesh‐free method with a direct nodal integration are improved considerably by the proposed stabilized conforming nodal integration method. It is also demonstrated that the Gauss integration method fails to meet IC in mesh‐free discretization. For this reason the proposed method provides even better accuracy than Gauss integration for Galerkin mesh‐free method as presented in several numerical examples. Copyright © 2001 John Wiley & Sons, Ltd.     

An Experimental Study of the Mechanical Behaviour of the ‘Conchyliates’ Shell‐Stone: Some Irregularities of the Size Effects

Abstract: A detailed experimental study of the size effect, i.e. of the dependence of the mechanical properties on the size of the (self‐similar) specimens used for the laboratory tests is presented in this paper for the case of a relatively soft natural building stone called ‘conchyliates’ (shell‐stone). ‘Conchyliates’ was used by ancient Greeks for the erection of the Zeus Temple at the Olympia archaeological site. The motive of the study was the need of the scientists working for a partial restoration of the monument for an in‐depth knowledge of the mechanical behaviour of both the original building material of the monument as well as of the material that could be used for the completion of damaged structural elements. During the study various classes of cylindrical ‘conchyliates’ specimens were subjected to uniaxial (unconfined) compression. It was concluded that the dependence of the peak stress of the material on the size of the specimen is not only very strong but it appears to be, also, non‐monotonous. In addition it was indicated that the size of the specimens also influences the elasticity modulus as well as the strain energy density in a more or less similar manner. On the contrary it is concluded that the slope of the strain energy density plotted versus strain is not seriously affected by the size of the specimen, at least for the working‐load portion of the stress‐strain graph.     

Continuous fatigue damage prediction of a rubber fibre composite structure using multiaxial energy‐based approach

This paper details an advanced method of continuous fatigue damage prediction of rubber fibre composite structures. A novel multiaxial energy‐based approach incorporating a mean stress correction is presented and also used to predict the fatigue life of a commercial vehicle air spring. The variations of elastic strain and complementary energies are joined to form the energy damage parameter. Material parameter α is introduced to adapt for any observed mean stress effect as well as being able to reproduce the well‐known Smith‐Watson‐Topper criterion. Since integration to calculate the energies is simplified, the approach can be employed regardless of the complexity of the thermo‐mechanical load history. Several numerical simulations and experimental tests were performed in order to obtain the required stress‐strain tensors and the corresponding fatigue lives, respectively. In simulations, the rubber material of the air spring was simulated as nonlinear elastic. The mean stress parameter α , which controls the influence of the mean stress on fatigue life, was adjusted with respect to those energy life curves obtained experimentally. The predicted fatigue life and the location of failure are in very good agreement with experimental observations.     

Sequentially linearizable initial‐boundary value problems for a neo‐hookean cylinder

Abstract

The sequential linearizabilities of some initial‐boundary value problems for the plane‐strain equations of motion of the neo‐Hookean solid are studied. The initial‐boundary value problems are formulated for a cylinder in plane‐strain condition and subjected to shear and radial deformations or tractions on its inner and outer surfaces. The results obtained extend the previous concept about the sequential linearizability of the governing equations for the neo‐Hookean solid to the sequential linearizability of initial‐boundary value problems for the governing equations.     

Modelling of reinforced‐concrete structures providing crack‐spacing based on X‐FEM,ED‐FEM and novel operator split solution procedure

In this work, we present a novel approach to the finite element modelling of reinforced‐concrete (RC) structures that provides the details of the constitutive behavior of each constituent (concrete, steel and bond‐slip), while keeping formally the same appearance as the classical finite element model. Each component constitutive behavior can be brought to fully non‐linear range, where we can consider cracking (or localized failure) of concrete, the plastic yielding and failure of steel bars and bond‐slip at concrete steel interface accounting for confining pressure effects. The standard finite element code architecture is preserved by using embedded discontinuity (ED‐FEM) and extended (X‐FEM) finite element strain representation for concrete and slip, respectively, along with the operator split solution method that separates the problem into computing the deformations of RC (with frozen slip) and the current value of the bond‐slip. Several numerical examples are presented in order to illustrate very satisfying performance of the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

Determination of dynamic rotation factor for DWTT specimens by strain analysis and hardness measurement

As to accurately ascertain the value of dynamic rotation factor r^*, strain analysis‐based measurement was performed on the bent low‐blow specimens by means of two approaches. (i) Surface strain analysis on the ligament indicates a critical transition zone from the necking to swelling, where the total strain reaches the minimum as undeformed material. (ii) Hardness measurement on the thickness‐reduction specimen also reflects a typical V‐shape distribution of interior plasticity along the ligament as observed from the surface, suggesting the location of true rotation centre relative to the neutral strain axis where the hardness is nearly invariable without any work hardening. As a result, the obtained value of r^* maintains nearly 0.45 for (B × 4B) size drop‐weight tear test‐type specimens after their crack initiation and propagation, well consistent with the values calculated from the slip‐line field theory.     

A Dual‐Responsive Mesoporous Silica Nanoparticle for Tumor‐Triggered Targeting Drug Delivery

A novel pH‐ and redox‐ dual‐responsive tumor‐triggered targeting mesoporous silica nanoparticle (TTTMSN) is designed as a drug carrier. The peptide RGDFFFFC is anchored on the surface of mesoporous silica nanoparticles via disulfide bonds, which are redox‐responsive, as a gatekeeper as well as a tumor‐targeting ligand. PEGylated technology is employed to protect the anchored peptide ligands. The peptide and monomethoxypolyethylene glycol (MPEG) with benzoic‐imine bond, which is pH‐sensitive, are then connected via “click” chemistry to obtain TTTMSN. In vitro cell research demonstrates that the targeting property of TTTMSN is switched off in normal tissues with neutral pH condition, and switched on in tumor tissues with acidic pH condition after removing the MPEG segment by hydrolysis of benzoic‐imine bond under acidic conditions. After deshielding of the MPEG segment, the drug‐loaded nanoparticles are easily taken up by tumor cells due to the exposed peptide targeting ligand, and subsequently the redox signal glutathione in tumor cells induces rapid drug release intracellularly after the cleavage of disulfide bond. This novel intelligent TTTMSN drug delivery system has great potential for cancer therapy.     

Highly Efficient (>10%) Flexible Organic Solar Cells on PEDOT‐Free and ITO‐Free Transparent Electrodes

A novel approach to fabricate flexible organic solar cells is proposed without indium tin oxide (ITO) and poly(3,4‐ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) using junction‐free metal nanonetworks (NNs) as transparent electrodes. The metal NNs are monolithically etched using nanoscale shadow masks, and they exhibit excellent optoelectronic performance. Furthermore, the optoelectrical properties of the NNs can be controlled by both the initial metal layer thickness and NN density. Hence, with an extremely thin silver layer, the appropriate density control of the networks can lead to high transmittance and low sheet resistance. Such NNs can be utilized for thin‐film devices without planarization by conductive materials such as PEDOT:PSS. A highly efficient flexible organic solar cell with a power conversion efficiency (PCE) of 10.6% and high device yield (93.8%) is fabricated on PEDOT‐free and ITO‐free transparent electrodes. Furthermore, the flexible solar cell retains 94.3% of the initial PCE even after 3000 bending stress tests (strain: 3.13%).