Partition of unity enrichment for bimaterial interface cracks

TLDR

The study develops partition of unity enrichment techniques for bimaterial interface cracks. The authors enrich finite element approximations with discontinuous and near‑tip asymptotic displacement functions via partition of unity, and evaluate mixed‑mode stress intensity factors using a domain interaction integral. The enrichment allows modeling without explicit crack meshing, captures the oscillatory singularity, and yields stress intensity factors that agree well with benchmark solutions. © 2004 John Wiley & Sons, Ltd.

Abstract

Abstract Partition of unity enrichment techniques are developed for bimaterial interface cracks. A discontinuous function and the two‐dimensional near‐tip asymptotic displacement functions are added to the finite element approximation using the framework of partition of unity. This enables the domain to be modelled by finite elements without explicitly meshing the crack surfaces. The crack‐tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The concept of partition of unity facilitates the incorporation of the oscillatory nature of the singularity within a conforming finite element approximation. The mixed‐mode (complex) stress intensity factors for bimaterial interfacial cracks are numerically evaluated using the domain form of the interaction integral. Good agreement between the numerical results and the reference solutions for benchmark interfacial crack problems is realized. Copyright © 2004 John Wiley & Sons, Ltd.