Volume integral equation method for multiple circular and elliptical inclusion problems in antiplane elastostatics

• Published in: Composites. Part B, Engineering Vol. 43; no. 3; pp. 1224 - 1243
• Main Authors: Lee, Jungki, Kim, Hye-Ran
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.04.2012; Elsevier
• Subjects: A. Fibres; Applied sciences; B. Anisotropy; C. Computational modelling; C. Numerical analysis; composite materials; Composites; elasticity (mechanics); equations; Exact sciences and technology; Forms of application and semi-finished materials; Laminates; methodology; Physicochemistry of polymers; Polymer industry, paints, wood; Technology of polymers; Volume Integral Equation Method (VIEM); C. Numerical analysis; A. Fibres; C. Computational modelling; Volume Integral Equation Method (VIEM); B. Anisotropy; Polymer; Numerical simulation; Modeling
• ISSN: 1359-8368; 1879-1069
• DOI: 10.1016/j.compositesb.2011.11.066

A Volume Integral Equation Method (VIEM) is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple isotropic and anisotropic circular/elliptical inclusions subject to remote antiplane shear. This method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central inclusion is carried out for square and hexagonal packing of isotropic and anisotropic inclusions. The effects of the number of isotropic and anisotropic inclusions and various fiber volume fractions on the stress field at the interface between the matrix and the central circular/elliptical inclusion are also investigated in detail. The accuracy of the method is validated by solving single isotropic and orthotropic circular/elliptical inclusion problems and multiple isotropic circular and elliptical inclusion problems for which solutions are available in the literature.