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A new method called the polarization approximation (PA) is constructed from the minimum energy principle; in this work, we construct a new approximation formula based on PA to determine the elastic moduli for three-phase composite materials with two different ellipse inclusions randomly distributed in the matrix. Some solutions with different approaches including PA, Mori–Tanaka approximation (MTA), differential approximations (DA), and fast Fourier transformation (FFT) method are constructed to estimate the elastic bulk and shear modulus of the three-phase composites in 2D. The numerical solutions using FFT analysis are compared with PA, DA, MTA, and Hashin–Shtrikman’s bounds. The comparison results show the effectiveness of the approximation methods, which makes MTA, PA, and DA useful with simplicity and ease of application.

The problem of computing the effective transport and mechanical properties of disordered materials, modeled by random or correlated percolation networks, is studied as an optimization problem. We show that calculating an optimal distribution of the potentials (voltages, displacements, etc.) throughout a disordered material that minimizes its total energy reduces the computation times for calculating the effective properties by a factor that depending on the morphology of the system, ranges from 3 to 73. Hence, this offers significant speed-up over the most efficient numerical methods currently available.

Various properties of substitutional alloys formed from aluminium and the platinum group metals (PGMs) are examined using density functional (D-F) theory and show strong variations depending on metal type. A similar pattern for the binary alloys is observed using molecular dynamics modeling employing Sutton Chen potentials. All results suggest that several of the PGMs could have superior properties to the presently used Ni₃Al alloy for high temperature applications. Some phases are predicted to be stable with extremely high melting temperatures (MTs).

In this study, the structural and unexplored elastic, electronic, optical and thermal properties of Pt-based alloys MPt₃ (M = Ti, Hf) and only optical and thermal properties of ZrPt₃ are subjected to investigation using the method of the first principles. The results of pressure dependence of mechanical and thermal properties are discussed. The electronic band structures and density of state data show metallic conductivity for all the compounds. The main contribution at Fermi level comes from Ti 3d and Zr 4d (for TiPt₃ and ZrPt${}_3)$ and Pt 5d (for HfPt${}_3)$ orbitals.

The materials’ optical reflectivity values, relatively high in the IR-visible-UV regions, range from $\sim$62% to 72% in the visible region which show better performance values in comparison to those of some representative materials PtAl₂, AuAl₂ and GdX₃ (X = In, Sn, Tl, Pb). The unexplored thermal behaviors are also investigated via quasi-harmonic Debye model at T = 0 and P = 0 as well as at elevated temperatures and pressures. In addition, when used as bonding materials, studied intermetallics with moderately high thermal expansion coefficients can match other substrates.

This coupled with the estimated thermal conductivities (k${}_{min}$) compared to several other species indicate that the intermetallics can be used in applications, such as thermal barrier coatings (TBC). This study has thus indicated possible alternative candidates for high-temperature applications which would initiate further research and development on the intermetallics under study.

In this paper, a mesh-free micromechanical material model for evaluation of woven fabric composite elastic moduli is developed. A new and realistic material model based on repeated unit approach with smooth fiber modes is presented. The mesh-free formulation is achieved through consideration of variation of potential energy in a similar manner to the finite element method. Radial basis functions are used as the approximation function in the mesh-free method developed. As no formal element mesh is used to model the matrix, fill and wrap in this approach, the simplicity in meshing is particularly notable. The results obtained for elastic moduli of woven fabric composites are shown to be accurate and in agreement to other available solutions.

In this paper, we develop a theoretical model for quantitative analysis of temperature-dependent heat capacity calculation of the magnetoresistance compounds RMnO₃ (R = La, Nd). The results on heat capacity obtained by us are in good agreement with the measured values. An effective interionic interaction potential (EIoIP) with the long-range Coulomb, van der Waals (vdW) interaction and short-range repulsive interaction up to second neighbor ions within the Hafemeister and Flygare approach was formulated to estimate the Debye and Einstein temperature and was found to be consistent with the available experimental data. In addition, the properties studied are the cohesive energy, molecular force constant, Restrahlen frequency and Gruneisen parameter. After characterizing thermal properties, a systematic investigation of elastic behavior has been undertaken and it has been found that the elastic moduli are decreasing continuously with increasing temperature.