Implicit boundary method for determination of effective properties of composite microstructures

A method that uses a structured grid to perform micromechanical analysis for determining effective properties of a composite microstructure is presented. This approach eliminates the need for constructing a mesh that has nodes along the interfaces between constituent materials of the composite. Implicit boundary method is used to ensure that interface conditions are satisfied at the material boundaries. In this method, solution structures for test and trial functions are constructed using approximate step functions such that the interface conditions are satisfied, even if there are no nodes on the material interface boundary. Since a structured grid does not conform to the geometry of the analysis domain, the geometry of the microstructure is defined independently using equations of the interface boundary curves/surfaces. Structured grids that overlap the geometry are easy to generate, and the elements in the grid are regular shaped and undistorted. A numerical example is presented to demonstrate that the proposed solution structure accurately models the solution across material interface, and convergence analysis is performed to show that the method converges as the grid density is increased. Fiber reinforced microstructures are analyzed to compute the effective elastic properties using both 2D and 3D models to show that the results match closely with the ones available in the literature.