Consistent immersed volumetric Nitsche methods for composite analysis

Generating quality body-fitting meshes for complex composite microstructures is a non-trivial task. In particular, micro-CT images of composites can contain numerous irregularly-shaped inclusions. Among the methods available, immersed boundary methods that discretize bodies independently provide potential for tackling these types of problems since a matching discretization is not needed. However, these techniques still entail the explicit parameterization of the interfaces, which may be considerable in number. In this work, immersed volumetric Nitsche methods are developed in order to avoid the difficulty of generating body fitting meshes for composite materials with complicated microstructures, and overcome the issues in the surface-type methods. These approaches are developed using Nitsche's techniques to enforce volumetric continuity between the inclusion and background domains. It is shown that the proposed weak forms are fully consistent with the strong form of the composite problem. The present approach permits C-0 approximations for the foreground discretization, and C-1 approximations for the background. The effectiveness of these methods is demonstrated by solving homogeneous and inhomogeneous composite benchmark problems, where it is shown that the non-symmetric version of Nitsche's approach is the most robust in all settings. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This work introduces immersed volumetric Nitsche methods to address the challenges of generating quality body-fitting meshes for complex composite microstructures. These methods enforce volumetric continuity and demonstrate consistency with the strong form of the composite problem, allowing for different levels of approximations. Experimental results show that the non-symmetric version of Nitsche's approach is the most robust in all settings.