Hierarchical interface-enriched finite element method: An automated technique for mesh-independent simulations

A hierarchical interface-enriched finite element method (HIFEM) is introduced for the mesh-independent treatment of problems with complex morphologies. The proposed method provides an automated framework to capture gradient discontinuities associated with multiple materials interfaces that are in a close proximity or contact, while using finite element meshes that do not conform to the problem geometry. While yielding an optimal precision and convergence rate, other principal advantages of HIFEM include the ease of implementation and the ability to compute enriched solutions for a variety of complex materials interface configurations. Moreover, the construction of enrichment functions in this method is independent of the number and sequence of materials interfaces introduced to the nonconforming mesh. An immediate benefit of this feature is the ability to add new materials phases to already enriched nonconforming elements, without the need to remove/modify existing enrichments or sub-elements. In addition to detailed convergence study, several example problems are presented to show the application of HIFEM for modeling various engineering problems, including woven composites, heterogeneous materials systems, and actively-cooled microvascular systems.