Volume Integral Equation Method Solution for Spheroidal Inclusion Problem.

Jungki Lee,Mingu Han

doi:10.3390/ma14226996

Abstract

In this paper, the volume integral equation method (VIEM) is introduced for the numerical analysis of an infinite isotropic solid containing a variety of single isotropic/anisotropic spheroidal inclusions. In order to introduce the VIEM as a versatile numerical method for the three-dimensional elastostatic inclusion problem, VIEM results are first presented for a range of single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under uniform remote tensile loading. We next considered single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix under remote shear loading. The authors hope that the results using the VIEM cited in this paper will be established as reference values for verifying the results of similar research using other analytical and numerical methods.

Highlights

The matrix and fibers in composites are usually made of isotropic material
In order to introduce the volume integral equation method (VIEM) as a versatile numerical method for the three-dimensional elastostatic inclusion problem, we first examine single isotropic/orthotropic spherical, prolate and oblate spheroidal inclusions in an infinite isotropic matrix subject to uniform remote tensile loading
Inside the inclusion can be arranged in ascending order of magnitude: (1) prolate spheroidal inclusion (a/b = c/b = 0.5), (2) prolate spheroidal inclusion (a/b = c/b = 0.75), (3) sphere, (4) oblate spheroidal inclusion (b/a = c/a = 0.75) and (5) oblate spheroidal inclusion (b/a = c/a = 0.5)

Summary

Introduction

The matrix and fibers in composites are usually made of isotropic material. in order to have higher strength and stiffness for commercial use, especially in the aerospace and automobile sectors, some constituents of metal matrix composites can be anisotropic.Since anisotropic materials are able to enhance mechanical properties toward orientation, certain mechanical properties (e.g., tensile strength) of anisotropic materials depend on orientation. The matrix and fibers in composites are usually made of isotropic material. In order to have higher strength and stiffness for commercial use, especially in the aerospace and automobile sectors, some constituents of metal matrix composites can be anisotropic. In titanium-silicon carbide (Ti-SiC) composites, the matrix is nearly isotropic, but the SiC fiber has strong anisotropy and a multilayered structure including an interphase and a core. Eshelby developed a simple and elegant method for solving the inclusion problem in isotropic solids in 1957 [1]. Eshelby found that the strain and stress field inside the ellipsoidal inclusion is uniform and has a closed-form solution, regardless of the material properties and initial eigenstrain [1].

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