Micromechanics of heterogeneous media
Date of Completion
High order local elastic fields based on two new micromechanics modeling approaches have been obtained for heterogeneous media problems. The problem is formulated in such a way that the effect of neighboring fibers in high volume fraction composites can be considered by introducing a homogeneous isotropic reference material with heterogeneity represented as fictitious body forces. For the homogeneous reference material local fields are formulated in terms of fundamental point load solutions (Green's function) leading to singular integral equations. The singularity is removed via a subtraction technique with the use of Eshelby solution and contour integrals. Besides this, Eshelby or Eshelby-like tensors can be simply constructed by this contour integral method. which can also be used to obtain the important conclusion that inside the isolated inclusion the stress and strain fields are uniform. Plus, this method can also be used to obtain Eshelby or Eshelby-like tensors for complicated fiber geometry.^ A Gauss quadrature rule based solution method was developed for cylindrical fiber composites. A high order polynomial representation of this local stress field was obtained. An isolated cylindrical inclusion problem was solved and compared with an analytical solution. In addition, the method is used to find the effective properties of a cylindrical fiber composite with rectangular packing as a function of fiber volume fraction. In both cases, promising results were obtained.^ For rectangular fiber composites, a high order subdomain method was developed based on a new closed form solution for a rectangular subdomain. Local fields were obtained as a piecewise quadratic polynomial. The solution yields average properties independent of the reference modulus as would be expected for an accurate solution and the effective transverse modulus vs. volume fraction is close to that from Christensen's analytical results. A test case was run for a layered laminate composite known to have a uniform stress field. The calculated results matched the exact solution to three significant digits. ^
Cheng, Jiangtian, "Micromechanics of heterogeneous media" (1997). Doctoral Dissertations. AAI9806167.