Performance assessment of hexahedral meshing methods for design and mechanical analysis of composite materials

Composite materials can be designed and modeled as material volumes with inclusions of several materials. These multiple inclusions are randomly distributed in a unit cube volume according to the material parameters (density, dimensions, orientation etc.). Then, the finite element (FE) analysis method is applied on the resulting structure to estimate the equivalent material properties. Therefore, these models should to be meshed prior to mechanical FE analysis. Automatic high quality hexahedral meshing is considered a very complex task. Hence, despite extensive research, currently there are no robust methods that can handle grain-based geometry. Meshing a composite material modeled by multiple inclusions presents a number of challenges: (a) the meshing needs to be robust to dimensions, position and orientation of the inclusions; (b) mesh continuity must be achieved on the boundaries between the volume (also known as the matrix) and the inclusions; (c) the mesh needs to approximate the original geometric model with high accuracy; and (d) high quality mesh elements are required for mechanical analysis. Structured and unstructured meshing methods can be used for handling this task. In this research two meshing methods were developed to generate high quality meshes: (a) structured meshing created by warping the grid according to the model's geometry, and (b) unstructured meshing created by projecting the nodes onto the boundaries of the inclusions to achieve exact geometric representation. The performance of these methods was then evaluated and compared on composite materials with ellipsoidal inclusions. Among the performance criteria for these methods are mesh element quality, geometry approximation error, stress concentrations near the boundaries, and computational complexity. The results indicate that the proposed methods can be used for design and mechanical analysis of composite materials. Moreover, in homogenization applications the structured warped mesh is compatible in terms of performance and element quality to the unstructured mesh.