Equivalent inclusions in micromechanics with interface energy effect

In order to apply classical micromechanics in predicting the effective prop- erties of nanocomposites incorporating interface energy, a concept of equivalent inclusion （EI） is usually adopted. The properties of EI are obtained by embedding a single inclusion with the interface into an infinite matrix. However, whether such an EI is universal for different micromechanics-based methods is rarely discussed in the literature. In this pa- per, the interface energy theory is used to study the applicability of the above mentioned EI. It is found that some elastic properties of the EI are related only to the properties of the inclusion and the interface, whereas others are also related to the properties of the matrix. The former properties of the EI can be applied to both the classical Mori-Tanaka method （MTM） and the generalized self-consistent method （GSCM）. However, the latter can be applied only to the MTM. Two kinds of new EIs are proposed for the GSCM and used to estimate the effective mechanical properties of nanocomposites.

An anisotropic micromechanics model for predicting the rafting direction in Ni-based single crystal superalloys

An anisotropic micromechanics model based on the equivalent inclusion method is developed to investigate the rafting direction of Ni-based single crystal superalloys. The micromechanical model considers actual cubic structure and orthogonal anisotropy properties. The von Mises stress, elastic strain energy density, and hydrostatic pressure in dif- ferent inclusions of micromechanical model are calculated when applying a tensile or compressive loading along the [001] direction. The calculated results can successfully pre- dict the rafting direction for alloys exhibiting a positive or a negative mismatch, which are in agreement with pervious experimental and theoretical studies. Moreover, the elastic constant differences and mismatch degree of the matrix and precipitate phases and their influences on the rafting direction are carefully discussed.

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.

Numerical study of contacts between a flat-ended punch and a half-space embedded with inhomogeneities

This paper presented a numerical approach to solving the problem of a flat-ended punch in contact with a half-space matrix embedded with multiple three dimensional arbitrary-shaped inhomogeneities.Based on the semi-analytical method(SAM)and the equivalent inclusion method,numerical procedures were developed and the effects of inclusion shape and distribution were analyzed.Fast Fourier transform technique was implemented to accelerate the calculation of surface deformation and subsurface stress.Interactions of inter-inclusions and inclusion-matrix were taken into account.Numerical results showed the presence of inhomogeneities(i.e.,microstructures in solids)indeed had a great effect on local contact pressure and a strong disturbance to the subsurface stress field in the vicinity of inclusions.The effects were dependent on the shape and distribution of inclusions and inter-inclusion interactions.The physical significance of this study is to provide an insight into the relation between the material microstructure and its response to the external load,and the solution approach and procedures may find useful applications,for example,the analysis of fatigue and crack propagation for composite materials,prediction of stress field in solids containing material defects,and study of the mechanism of chemical-mechanical polish(CMP)for inhomogeneous materials,etc.

Semi-analytical Modeling of the Influence of Macro Bending Effects on Micro Contact-Inhomogeneity Problems

This study examines the effects of macroscopic bending and microscopic contact loading in inhomogeneous materials using a semi-analytical model based on Eshelby’s equivalent inclusion method.The model accounts for bending effects through the beam theory,with bending stress included in the Eshelby’s equivalent inclusion equations.The macroscopic displacement resulting from bending effects is incorporated into the microscopic contact solver,and the final displacement is determined using the conjugate gradient method in an iterative solution.Computational efficiency can be improved by incorporating the discrete convolution and fast Fourier transform.The core scheme is validated using the finite element method,yielding accurate and efficient results for bending-contact problems in inhomogeneous materials.Simulations reveal the interplay between bending,contact loading,and inhomogeneity,as stress around the inhomogeneity alters and the stress concentration area expands under increasing bending moments.Conversely,low-magnitude negative bending moments reduce both contact pressure and stress around the inhomogeneity.The position where inhomogeneities are least affected shifts from the neutral surface depending on the coupling effect.The model provides a valuable bridge for connecting the macroscopic bending effect and microscale contact-inhomogeneity problems by visualizing stress fields and assessing pressure distributions.

Study and application of temporal index technology

This paper addresses the mathematical relation on a set of periods and temporal indexing construc- tions as well as their applications.First we introduce two concepts, i.e.the temporal connection and temporal inclusion, which are equivalence relation and preorder relation respectively.Second, by study- ing some basic topics such as the division of ＂large＂ equivalence classes and the overlaps of preorder relational sets, we propose a temporal data index model （TDIM） with a tree-structure consisting of a root node, equivalence class nodes and linearly ordered branch nodes.Third, we study algorithms for the temporal querying and incremental updating as well as dynamical management within the framework of TDIM.Based on a proper mathematical supporting, TDIM can be applied to researching some significant practical cases such as temporal relational and temporal XML data and so on.