Novel implementation of homogenization method to predict effective properties of periodic materials

Representative volume element （RVE） method and asymptotic homogenization （AH） method are two widely used methods in predicting effective properties of pe- riodic materials. This paper develops a novel implementa- tion of the AH method, which has rigorous mathematical foundation of the AH method, and also simplicity as the RVE method. This implementation can be easily realized using commercial software as a black box, and can use all kinds of elements available in commercial software to model unit cells with rather complicated microstructures, so the model may remain a fairly small scale. Several examples were car- fled out to demonstrate the simplicity and effectiveness of the new implementation.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material

In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional（2-D） periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended averaging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell.In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellular solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material.

EFFECT OF STRUCTURE OF FUNCTIONAL POLYMER ACTIVE MATERIALS ON PROPERTIES OF GADOLINIUM ION SELECTIVE ELECTRODE

In this paper,the functional polymeric active materials were prepared by the grafting copolymerization and their structure and properties were studied.The results show that the structure and properties of these ac- tive materials have the relative large effects on the properties of gadolinium ion selective electrodes.

Effect of trabecular bone material properties on ultrasonic backscattering signals

In this study, ultrasonic backscattering signals in cancellous bones were obtained by finite difference time domain （FDTD） simulations, and the effect of trabecular material properties on these signals was analyzed. The backscatter coefficient （BSC） and integrated backscatter coefficient （IBC） were numerically investigated for varying trabecular bone material properties, including density, Lame coefficients, viscosities, and resistance coefficients. The results show that the BSC is a complex function of trabecular bone density, and the IBC increases as density increases. The BSC and IBC increase with the first and second Lame coefficients. While not very sensitive to the second viscosity of the trabeculae, the BSC and IBC decrease as the first viscosity and resistance coefficients increase. The results demonstrate that, in addition to bone mineral density （BMD） and microarchitecture, trabecular material properties significantly influence ultrasonic backseattering signals in cancellous bones. This research furthers the understanding of ultrasonic backscattering in cancellous bones and the characterization of cancellous bone status.

Macro-architectured cellular materials： Properties, characteristic modes, and prediction methods

Macro-architectured cellular （MAC） material is defined as a class of engineered materials having configurable cells of relatively large （i.e., visible） size that can be architecturally designed to achieve various desired material properties. Two types of novel MAC materials, negative Poisson＇s ratio material and biomimetic tendon reinforced material, were introduced in this study. To estimate the effective material properties for structural analyses and to optimally design such materials, a set of suitable homogenization methods was developed that provided an effective means for the multiscale modeling of MAC materials. First, a strain-based homogenization method was developed using an approach that separated the strain field into a homogenized strain field and a strain variation field in the local cellular domain superposed on the homogenized strain field. The principle of virtual displacements for the relationship between the strain variation field and the homogenized strain field was then used to condense the strain variation field onto the homogenized strain field. The new method was then extended to a stress-based homogenization process based on the principle of virtual forces and further applied to address the discrete systems represented by the beam or frame structures of the aforementioned MAC materials. The characteristic modes and the stress recovery process used to predict the stress distribution inside the cellular domain and thus determine the material strengths and failures at the local level are also discussed.