A meshfree immersed variational multiscale method for perfectly bonded interfaces

• Existing methods can give oscillatory tractions on immersed interfaces. • An immersed variational multiscale method is derived in a meshfree setting. • The proposed method is primal, like Nitsche’s method, but is more robust. • Good accuracy is achieved in both bulk domain and interfacial quantities. Composites are ubiquitous in many engineering applications, and computing stresses near material interfaces is crucial for predicting and understanding meso- and micro-structural failure in these materials. While many notable approaches to this problem are available, stable interfacial tractions are still difficult to achieve in numerical simulations. This work presents a simplified immersed variational multiscale (SIVMS) method for interfaces that achieves stable, convergent results for the normal traction. The convergence behavior in both the bulk domain fields and interfacial tractions is investigated for SIVMS and is compared to conventional methods such as the Lagrange multiplier method and Nitsche’s method. The difficulty in selecting appropriate values of parameters for Nitsche’s method is highlighted. In contrast, SIVMS provides stabilization that emanates naturally from the assumed fine-scale basis functions. The proposed SIVMS method is free from ad-hoc parameters and provides good accuracy and stability in interfacial tractions. Several benchmark test cases are presented to show the effectiveness and confirm the range of applicability of the proposed method.