Isotoxal star-shaped polygonal voids and rigid inclusions in nonuniform antiplane shear fields. Part II: Singularities, annihilation and invisibility

TL;DR

This paper analytically investigates stress singularities, annihilation, and invisibility in star-shaped voids and inclusions under nonuniform shear, revealing conditions for stress-free corners and invisible inclusions that enhance material strength.

Contribution

It identifies specific geometries and loadings that eliminate stress singularities and achieve invisibility, advancing design strategies for ultra-resistant composite materials.

Findings

Certain geometries eliminate stress singularities at corners.

Conditions for stress annihilation where stress vanishes at inclusion tips.

Invisibility conditions where inclusions do not perturb the ambient stress.

Abstract

Notch stress intensity factors and stress intensity factors are obtained analytically for isotoxal star-shaped polygonal voids and rigid inclusions (and also for the corresponding limit cases of star-shaped cracks and stiffeners), when loaded through remote inhomogeneous (self-equilibrated, polynomial) antiplane shear stress in an infinite linear elastic matrix. Usually these solutions show stress singularities at the inclusion corners. It is shown that an infinite set of geometries and loading conditions exist for which not only the singularity is absent, but the stress vanishes ('annihilates') at the corners. Thus the material, which even without the inclusion corners would have a finite stress, remains unstressed at these points in spite of the applied remote load. Moreover, similar conditions are determined in which a star-shaped crack or stiffener leaves the ambient stress completely unperturbed, thus reaching a condition of 'quasi-static invisibility'. Stress annihilation and invisibility define optimal loading modes for the overall strength of a composite and are useful for designing ultra-resistant materials.