Calculations of single-crystal elastic constants made simple

We present an efficient method to obtain single-crystal elastic constants. Using the method, the computation effort for the complete set of elastic constants (21 components for a triclinic crystal) of a crystal under a given strain state is similar to that for the bulk modulus, where the latter is normally calculated first together with the equilibrium volume by fitting the volume-dependent energy to an equation of state. The idea in the efficiency improvement is to apply linear-independent coupling strains to a crystal, and to extract the complete set of elastic constants simultaneously. For the new method, a single set of strains are universally applicable to all crystals, and less number of strains are needed for crystals of higher symmetry. Calculated single-crystal elastic constants of cubic diamond, hexagonal osmium, orthorhombic TiSi₂ and monoclinic Mg₅Si₆ are given as examples.     

Physical Properties of Glass Fiber Reinforced Polymer Rebars in Compression

Forty-five glass fiber reinforced polymer (GFRP) rebars were tested in compression to determine their ultimate strength and Young’s modulus. The rebars (or C-bars), produced by Marshall Industries Composites, Inc., had an outside diameter of 15 mm (#15 rebar), and unbraced lengths varying from 50 to 380 mm. A compression test method was developed to conduct the experiments. Three failure modes, that are directly related to the unbraced length of the rebar, are identified as crushing, buckling, and combined buckling and crushing. The crushing region represents the failure mode a GFRP rebar would experience when confined in concrete under compression. The experimental results showed that the ultimate compressive strength of the #15 GFRP rebar failing by crushing is approximately 50% of the ultimate tensile strength. Based on a very limited number of tests, in which strain readings were acceptable, Young’s modulus in compression was found to be approximately the same as in tension.     

Mechanics of extended continua: modeling and simulation of elastic microstretch materials

The investigation of microstretch and micromorphic continua (which are prominent examples of so-called extended continua) dates back to Eringens pioneering works in the mid 1960, cf. (Eringen in Mechanics of micromorphic materials. Springer, Berlin Heidelberg New York, pp 131–138, 1966; Eringen in Int J Eng Sci 8:819–828; Eringen in Microcontinuum field theories. Springer, Berlin Heidelberg New York, 1999). Here, we re-derive the governing equations of microstretch continua in a variational setting, providing a natural framework within which numerical implementations of the model equations by means of the finite element method can be obtained straightforwardly. In the application of Dirichlets principle, the postulation of an appropriate form of the Helmholtz free energy turns out to be crucial to the derivation of the balance laws and constitutive relations for microstretch continua. At present, the material parameters involved in the free energy have been assigned fixed values throughout all numerical simulations—this simplification is addressed in detail as the influence of those parameters must not be underestimated. Since only few numerical results demonstrating elastic microstretch material behavior in engineering applications are available, the focus is here on the presentation of numerical results for simple twodimensional test specimens subjected to a plane strain condition and uniaxial tension. Confidence in the simulations for microstretch materials is gained by showing that they exhibit a “downward-compatibility” to Cosserat continuum formulation: by switching off all stretch-related effects, the governing set of equations reduces to the one used for polar materials. Further, certain material parameters can be chosen to act as penalty parameters, forcing stretch-related contributions to an almost negligible range in a full microstretch model so that numerical results obtained for a polar model can be obtained as a limiting case from the full microstretch model.     

Substitution and price elasticity estimates using inter-country pooled data in a translog cost model

Pooled data across several developing countries and the U. S. were used to estimate long-run substitution and price elasticities in a translog framework for the paper, iron and steel, and aggregate manufacturing industries. While the quality of the estimates varies across the several industry-specific models, the results suggest higher values for these elasticities than appear commonly used in integrated assessment models. Estimates of own-price elasticities of energy range from − 0.80 to − 1.76 and are comparable to estimates from previous econometric studies in the context of developed countries (− 0.77 to − 0.87). Substitution elasticities show wider variation across countries and industries. For energy and capital they range from − 1.96 to 9.80, for labor and energy from 2.61 to 7.11, and for energy and material from − 0.26 to 2.07.     

Analysis of equivalent elastic modulus of asymmetrical honeycomb

In this report, elastic moduli of honeycomb consisting of asymmetrical hexagonal cells are studied by using a theoretical approach and the finite element method (FEM). Based on the change in the shape of the hexagonal cell, explicit equations describing the equivalent elastic moduli of honeycomb with cell wall parallel to the y-axis are proposed. In the analysis of honeycomb deformation, the shear deformation was considered in addition to bending deformation and tensile deformation. As a result, the equivalent elastic moduli could be calculated with extremely high precision.     

Spatial mismatch and the affordability of public transport for the poor in Singapore’s new towns

Singapore has redeveloped its Central Area into business districts and relocated the affected population to new towns. Unfortunately, this strong center policy has hindered the development of employment sub-centers. Most jobs are located in the Central Area, resulting in a spatial mismatch that the government is attempting to address by building a world-class public transport system. However, the poor not only face affordability problems and long travel times for employment, but they are also experiencing a shrinking supply of employment due to economic restructuring. Route tests were conducted, and the results indicate that the poor, who generally choose to travel by bus, have to spend up to 9.8% of their household income per month and 70 min per trip from their neighborhoods to the city center. Those who take the hub-and-spoke network have to spend 13.2% of household income and take 60 min for similar trips. To increase the job-seeking range of these people, they should be offered concessions to encourage use of the hub-and-spoke network. The government should also build a light-rail transit line to pass through the Central Catchment Nature Reserve to connect employment sub-centers.     

肉类弹性测定方法的研究

文章阐述了使用高精密度的TZ-XTZi物性仪测定肉类弹性的方法。比较了不同测定方法的弹性数据与感官对照之间的相关性，试验结果表明一次压缩过程中的最在力来表示肉的弹性较为恰当。     

Methods for analysing partial contact between surfaces

This paper reviews methods available for the numerical solution of contact mechanics problems, in particular, those in which the extent of the contact(s) is not known at the start of the analysis. A new objective function is proposed which is generally smooth and which enables contact mechanics problems to be solved by unconstrained minimisation, in spite of the non-linear boundary condition at the interface. The application of the method to plane periodic elastic contacts, and the author's previously published M(x) formulation of such cases, is demonstrated in detail.     

A mixed least squares method for solving problems in linear elasticity: theoretical study

 In a previous paper we proposed a mixed least squares method for solving problems in linear elasticity. The solution to the equations of linear elasticity was obtained via minimization of a least squares functional depending on displacements and stresses. The performance of the method was tested numerically for low order elements for classical examples with well known analytical solutions. In this paper we derive a condition for the existence and uniqueness of the solution of the discrete problem for both compressible and incompressible cases, and verify the uniqueness of the solution analytically for two low order piece-wise polynomial FEM spaces. Received: 20 January 2001 / Accepted: 14 June 2002 The authors gratefully acknowledge the financial support provided by NASA George C. Marshall Space Flight Centre under contract number NAS8-38779.     

Numerical Validation of an Elastoplastic Formulation of the Conventional Limit Pressure Measured with the Pressuremeter Test in Cohesive Soil

An elastoplastic pressuremeter theory for cohesive soil has been used in the design of construction, such as retaining walls, slope stability, or foundation engineering. This theory takes into account the plasticity along the vertical and horizontal planes and allows for the determination of the conventional limit pressure. We compute here the conventional limit pressure using the Plaxis program to check the validity of the theoretical results. First, we present the theory used for the interpretation of the pressuremeter test in cohesive soil and its extension to the conventional limit pressure, which is defined as the pressure at the borehole wall for a volume increase ΔV equal to the initial volume of the borehole. One of the main results is the theoretical expression of the conventional limit pressure. This volume variation is linked to a radial strain of ?1. This conventional limit pressure can be directly measured with the pressuremeter, whereas the theoretical limit pressure is expressed as an infinite expansion and cannot be directly measured. Then, we validate this theory by using finite elements, and determine the conventional limit pressure with the Tresca standard model of Plaxis, which is compared to the theoretical expression. Conclusions are drawn on the validity of this new theory which allows the measurement and the control of the shearing modulus and shear strength of the natural soil.