A mixed SBFEM for stress singularities in nearly incompressible multi-materials

• A mixed scaled boundary finite element formulation with near incompressibility.
• The formulation does not require any mesh-dependent and stabilization parameters.
• It allows direction determination of generalized stress intensity factors.
• It can model strong discontinuities near crack/notch, interface crack/notch tips.
• Avoids volumetric locking and numerical oscillations at near incompressible limit.

In this paper, a mixed formulation based on the scaled boundary finite element method (SBFEM) is proposed for nearly incompressible linear elasticity. The problems with strong discontinuities in nearly incompressible linear multi-materials are analyzed. The proposed technique avoids volumetric locking and non-physical pressure oscillations at near incompressible limit without requiring any mesh-dependent or stabilization parameters. The pressure field is introduced but it is not independently unknown in the proposed technique. The pressure and displacement are interpolated identically on the boundary. Standard polynomial shape functions and high order line-elements are used. The governing equation of mixed SBFEM in displacement is derived based on the virtual work principle. The displacement, stress and pressure fields along the radial direction are represented analytically, which permits the stress intensity factors to be directly evaluated by definition.