Model and analysis of size-stiffening in nanoporous cellular solids

The size of the struts in nanoporous cellular solids typically has a secondary influence on the stiffness of the solids, but it leads to significant stiffening when it is on the same order as the higher-order material parameter. We examined this size-dependence using the higher-order finite-element method (FEM) in this study. Mathematical analysis showed that the displacement field that satisfies the conventional Lame equation can serve as a displacement field template in higher-order FEM. Benchmarking studies showed that results from simulations of beam bending and rod torsion using this FEM approach were in good agreement with results from analytical solutions and experiments. Using this approach, we showed that the stiffness of cellular solids is strongly affected by the cellular arrangement and the density when the cell size is on the order of the higher-order material parameter and that the stiffening behavior in nanoporous polyimide can be explained using higher-order theory. The FEM results also showed that a porous solid with half the weight can be engineered to become as stiff as a fully dense solid if the porous microarchitecture is tailored to take advantage of higher-order stiffening.     

A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

The capacitated lot-sizing problem with set-up carryover and set-up splitting (CLSP-SCSS) is formulated as a mixed integer linear program. We define set-up carryover as the production of a product that is continued over from one period to another without incurring an extra set-up. Set-up splitting occurs when the set-up for a product is started at the end of a period and completed at the beginning of the next period. We allow product dependent set-ups. Initial experimentation highlights the importance of including set-up splitting in the CLSP model. In 12 out of the 18 problem instances tested, our model yielded better solutions or removed infeasibility when compared with a CLSP model without set-up splitting.     

At the limit of polychromatic microdiffraction

With a high-energy 3rd generation source like the Advanced Photon Source (APS), it is possible to push the performance of polychromatic microdiffraction far beyond current levels and to approach the intrinsic limit of the technique based on sample damage and the diffraction limit of X-rays. We describe ongoing efforts to improve the spatial, temporal and momentum transfer resolution of polychromatic microdiffraction on beamline 34-ID-E at the APS. The goal of this effort is to provide high-resolution images of 3D crystal structures over sufficient volumes and with sufficient detail to clarify the underlying physics of inhomogeneous structure and evolution on mesoscopic length scales. The performance of a high-speed amorphous Si area detector system and the ongoing development of advanced focusing optics will be described and discussed in light of the ultimate limits set by the physics of X-rays and materials, and in light of opportunities to field specialized insertion devices and optics for polychromatic microdiffraction.     

A hybrid model for prismatic solids

A finite prism approach for the approximate analysis of three-dimensional solids is proposed. The approach is based on a semi-algebraic assumed stress hybrid model, according to Pian's scheme. Prismatic solids with various end conditions can be analysed with a traditional matrix-displacement procedure, thus enlarging the possibilities offered by analogous compatible models.     

A self-consistent model for microcrack-weakened solids

The paper focuses on the formulation of a self-consistent process model for a perfectly elastic solid weakened by an ensemble of microcracks. The derivation is restricted to the plane stress and strain, and monotonically increasing tensile loads. The proposed formulation does not require introduction of additional, physically unidentifiable, ‘material’ parameters.     

A mixed integer linear programming model for set-up reduction superstructures

The objective of this research is to introduce the concept of a set-up reduction superstructure and evaluate its utility in set-up reduction projects. For a given set-up project, consisting of several interdependent activities as well as existing ones, a superstructure is defined. For this superstructure, a corresponding mixed integer linear programming model is developed with a view to selecting the optimum set-up project. The resulting model is applied to the set-up reduction problem in a real example of the fabrication in a CNC lathe of a vibration reduction pulley for lorry motors. The model is implemented in the Mathematica platform. It is shown that the set-up reduction superstructure is a useful concept in practice.     

A solution to the multiple set-up problem

This note finds the optimal order quantity for the multiple set-up problem. The solution is obtained by a direct method.     

New set-up for in-plane permeability measurement

The determination of accurate permeability values is critical to process simulations for Resin Transfer Molding (RTM). New instrumentation is presented in this paper for high throughput permeability measurements. The design extends the original work of Hoes [Hoes K. Development of a new sensor-based set-up for experimental permeability identification of fibrous media, PhD thesis, Vrije Universiteit Brussels, Brussels, 2003] with a new sensor design, a much larger sensor pattern, and new analysis software. For example, the new analysis software is more robust than previous versions in that it will compute the flow front orientation angle rather than assume the angle as given by the user. The new set-up was used to measure the permeability of a basalt woven 3/1 twill fabric. When compared with previous work on 2/2 twill and plain woven fabrics, a relationship was observed between the breadth of the anisotropy distribution, the correlation between the principle components of the permeability tensor, and the fabric structure. Such a relationship has implications for manufacturing reliability, and may help explain why some fabrics process much more consistently than others.     

Electron microdiffraction studies of zirconia particles

A batch of zirconia was prepared at a pH of 2.95 using a sol-gel technique. The crystal structures formed during 500 °C calcination was followed by X-ray diffraction. The tetragonal phase was the major component after the initial calcination period of 15.5 h; however, it gradually transformed to the monoclinic crystal form during 200 h of calcination at 500 °C. Electron microdiffraction was employed in the present investigation to determine the crystal structure of individual particles, and to identify whether these particles contained twin variants. A technique has been developed to get a dispersion of agglomerated particles by condensing and spreading the beam on the agglomerates at 200 kV. The data revealed that some of the individual zirconia particles are featureless and some of them appear to contain single or multiple twin variants.     

A multiscale approach for modeling crystalline solids

In this paper we present a modeling approach to bridge the atomistic with macroscopic scales in crystalline materials. The methodology combines identification and modeling of the controlling unit processes at microscopic level with the direct atomistic determination of fundamental material properties. These properties are computed using a many body Force Field derived from ab initio quantum-mechanical calculations. This approach is exercised to describe the mechanical response of high-purity Tantalum single crystals, including the effect of temperature and strain-rate on the hardening rate. The resulting atomistically informed model is found to capture salient features of the behavior of these crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate. This revised version was published online in June 2006 with corrections to the Cover Date.     

A constitutive equation for non-linear electro-active solids

Summary Electro-active solids are solids that are either infused with electrorheological fluids or embedded with electrically conducting particles, the body as a whole however conducting negligible current. In this paper, we provide a mathematical framework, within the context of continuum mechanics, for the study of electro-active solids. The theory assumes that the body can be considered as a continuum, in the sense of homogenization, which is isotropic, incompressible, elastic and is capable of responding to an electric field. Appealing to standard techniques in continuum mechanics, we obtain a constitutive relation for the stresses in terms of the deformation and electric field. This is used in a study of triaxial extension, simple shear and anisotropy induced by the electric field.     

A plasticity theory for fluid-saturated porous solids

A theory of plastic flow is developed for an elastic-perfectly plastic porous solid with its intercommunicating void spaces filled with a viscous fluid. The constitutive equations are established where full use is made of the thermodynamical equations. The final result of the paper is the complete set of equations of the theory and the boundary conditions for the medium in question.     

A quasi-correspondence principle for Quasi-Linear viscoelastic solids

In this paper we show that the correspondence principle that allows one to obtain solutions to boundary-initial value problems for Linear viscoelastic solids from solutions to that for a linearized elastic solid can be extended, in many circumstances, to the case of the Quasi-Linear viscoelastic solids introduced by Fung. We illustrate the ability to generalize the correspondence principle by considering a variety of problems including torsion, transverse loading of beams and several problems that involve a single non-zero stress component. This extension is however not possible for certain classes of problems and we present a specific example where the correspondence principle breaks down. The correspondence principle between Linear elasticity and Linear viscoelasticity also breaks down under certain conditions, however the correspondence between the solutions for Linear viscoelasticity and Quasi-Linear viscoelasticity is even more fragile in that it breaks down while the classical correspondence works, and hence we refer to the correspondence as a quasi-correspondence principle.     

A constitutive model for compressible elastomeric solids

A non-linear thermo-elastic constitutive model for the large deformations of isotropic materials is formulated. This model is specialized to account for the physics and thermodynamics of the elastic deformation of rubber-like materials, and based on these molecular considerations a constitutive model for compressible elastomeric solids is proposed. The new constitutive model generalizes the incompressible and isothermal model of Arruda and Boyce (1993) to include the compressibility and thermal expansion of these materials. The model is fit to existing experimental data on vulcanized natural rubbers to determine the material parameters for the rubbers examined. The fit between the simple model and the data is found to be very good for large stretches and moderate volume changes.List of symbols x\s=f(p) Deformation function - p Material point of a body in a reference configuration - x Place occupied by material point p in the current configuration - F(p)\eq(\t6/\t6p) f(p) Deformation gradient - J\s=det F\s>0 Determinant of F - F\s=RU\s=VR Polar decompositions of F - U, V Right and left stretch tensors; positive definite and symmetric - R Rotation tensor; proper orthogonal - U= _1–1 ³ ₁ ² r₁r₁ Spectral representation of U - V= ₁₌₁ ³ _t ² 1_t1₁ Spectral representation of V - _t > 0 Principal stretches - {r_i} Right principal basis - {l_i} Left principal basis - C\s=F ^T F, B\s=FF ^T Right and left Cauchy-Green strain tensors - \gq\s>0 Absolute temperature - \ge Internal energy density/unit reference volume - \gh Entropy density/unit reference volume - \gy\s=\ge\t-\gq\gh Helmholtz free energy/unit reference volume     

Computer-aided set-up planning for machining centres configuration

One of the key issues in defining the optimal configuration of a machining centre is the problem of determining the minimal number of set-ups for the part types to be machined. This paper proposes a method to define near-optimal set-up plans for prismatic workpieces when multiple parts can be mounted on the same pallet. Set-ups are determined taking into account the accessibility of the machining directions of the workpiece and the technological constraints among the required operations. The technological constraints are divided into three types: constraints that force the operations to share the same set-up, precedence constraints that cannot be violated in the sequence of set-ups, and constraints that translate technological preferences and that might be sacrificed to optimize the set-up plan. The technological constraints are analysed with a graph-based approach. The method proposes a solution for three-, four- and five-axis machines. The set-up plan for three axes is the starting point to determine the solutions for four- and five-axis machines: the set-up plan for four and five axes results from the combination of set-ups of the three-axis machine. Alternative solutions with the minimal number of set-ups are determined. Each solution specifies the orientation of the workpiece on the pallet fixture in each set-up, the operations to be executed in each set-up and the precedence relations among set-ups. Starting from the results of the set-up planning, the configuration of the pallet can be defined and taking into account the pallet configuration, the optimal machining centre for specific manufacturing needs is selected.     

Group set-up for printed circuit board assembly

The current practice in the assembly of electronic components on printed circuit boards (PCBs) is serial production, a process characterized by very long set-up times. However, with the advent of efficient on-line process information, new production control methods are now possible. This paper proposes a different production method, called the group set-up (GSU) method, which can significantly reduce set-up times. The traditional and the GSU production methods are compared, and it is shown that the GSU always performs better than the traditional method in terms of total production flow (throughput) and labour time. However, the traditional method performs better than the GSU in terms of work in process (WIP) inventory; and in some cases, in terms of makespan (lead time). A detailed analysis for a small number of PCBs is presented.     

A novel experimental set-up for turbidity sensing based on plastic optical fibre

A novel set-up for remote sensing the turbidity of a solution using plastic optical fibres together with a mirror is proposed. The authors have estimated turbidity of a liquid in terms of the nephelometric turbidity unit – NTU, a standard unit that relates the solution appearance with its turbidity for two proposed set-ups. Its performance was also investigated using clay sample measurements over a concentration range of 0–10 g/L. The proposed set-ups are useful for detection of suspended particles in a solution even in small quantities due to its high sensitivity, simplicity and robustness.     

A two-step sol-gel method for synthesis of nanoporous TiO2

This article reports a study of the effects of synthesis parameters on the preparation and formation of mesoporous titania nanopowders by employing a two-step sol-gel method. These materials displayed crystalline domains characteristic of anatase. The first step of the process involved the hydrolysis of titanium isopropoxide in a basic aqueous solution mediated by neutral surfactant. The solid product obtained from step 1 was then treated in an acidified ethanol solution containing the same titanium precursor to thicken the pore walls. Low pH and higher loading of the Ti precursor in step 2 produced better mesoporosity and crystallinity of titanium dioxide polymorphs. The resultant powder exhibited a high surface area (73.8 m2/g) and large pore volume (0.17 cm3/g) with uniform mesopores. These materials are envisaged to be used as precursors for mesoporous titania films as a wide band gap semiconductor in dye-sensitized nanocrystalline TiO2 solar cells.     

A modified framework for modelling set-up carryover in the capacitated lotsizing problem

In this note, a modified framework to model set-up carryovers in the capacitated lotsizing problem is presented. The proposed framework allows product dependent set-up times and costs to be incorporated. This is an extension of an earlier published work on modelling set-up carryovers for the constant set-up time scenario. An example to illustrate the modified framework is also provided.