Consistent immersed volumetric Nitsche methods for composite analysis

• Published in: Computer methods in applied mechanics and engineering Vol. 385; p. 114042
• Main Authors: Wang, Jiarui, Zhou, Guohua, Hillman, Michael, Madra, Anna, Bazilevs, Yuri, Du, Jing, Su, Kangning
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2021; Elsevier BV
• Subjects: Approximation; Composite; Composite materials; Computed tomography; Discretization; Immersed; Inclusions; Microstructure; Nitsche; Non-symmetric Nitsche; Parameterization; Volumetric; Non-symmetric Nitsche; Composite; Volumetric; Microstructure; Nitsche; Immersed
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114042

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 C0 approximations for the foreground discretization, and C1 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. •Symmetric and non-symmetric volumetric immersed Nitsche methods proposed.•The proposed weak forms attest to the composite strong form.•Non-conforming discretizations are admissible for background and foreground domains.•The intersection of quadrature domains does not need to be computed or considered.•Explicit definition of interfaces is not required.