Wedge-tip singularity of bi-materials under large deformation

Wedges are ubiquitous in engineering structures. Stress concentration near wedge tips plays a pivotal role in structural failure. Wedge-tip fields in linear elastic materials have been well characterized. Analysing wedge-tip fields in nonlinear materials undergoing large deformation remains challenging. In this work, we develop an asymptotic approach to solve for bi-material wedge-tip fields using a hyperelastic constitutive law. We obtain generalized solutions for bi-material wedge-tip fields under arbitrary combinations of material properties and wedge angles under large deformation. From theoretical solutions, we identify key characteristics of wedge-tip fields, including two parameters analogous to stress intensity factors in linear elasticity. Examining the stress fields of wedge tips, we reveal complex interdependencies between the singularity index, shear modulus ratio and wedge angle. We further conduct finite element analysis (FEA) and achieve good agreement with theoretical predictions on the stress singularity and amplitude. These findings establish a foundation for investigating failure mechanisms and developing strength criteria of materials.