Multimaterial wedges are frequently observed in composite materials. They consist of
two or more sectors of dissimilar materials joined together, whose interfaces
converge at the same vertex. Due to the mismatch in material properties
such as Young’s modulus, thermal conductivity, dielectric permittivity, or
magnetic permeability, these geometrical configurations can lead to singular
fields at the junction vertex. This paper discusses mathematical analogies,
focused on singular harmonic problems, between antiplane shear problem in
elasticity due to mode III loading or torsion, the steady-state heat transfer
problem, and the diffraction of waves in electromagnetism. In the case of a
single material wedge, a mathematical analogy between elasticity and fluid
dynamics is also outlined. The proposed unified mathematical formulation is
particularly convenient for the identification of common types of singularities
(power-law or logarithmic type), the definition of a standardized method
to solve nonlinear eigenvalue problems, and the determination of common
geometrical and material configurations allowing the relief or removal of different
singularities.