# Torsion of elastic solids with sparse voids parallel to the twist axis

## TL;DR

This paper derives analytical solutions for stress concentration around voids in elastic solids under torsion, revealing special behaviors like stress annihilation and validating results with finite element simulations for practical design applications.

## Contribution

It provides new closed-form expressions for stress factors around various void shapes in torsion, including special cases with stress singularity removal, validated by finite element analysis.

## Key findings

- Analytical expressions accurately predict stress intensification.
- Special void configurations can eliminate stress singularities.
- Finite element simulations confirm the validity of the analytical solutions.

## Abstract

With the purpose of investigating a linear elastic solid containing a dilute distribution of cylindrical and prismatic holes parallel to the torsion axis, the full-field solution for an infinite elastic plane containing a single void and subject to torsion is derived. The obtained solution is exploited to derive the analytic expressions for the Stress Concentration Factor (SCF) related to the presence of an elliptical hole, for the Stress Intensity Factor (SIF) for hypocycloidal-shaped hole and star-shaped cracks, and for the Notch Stress Intensity Factor (NSIF) for star-shaped polygons. Special sets of the void location are obtained for which peculiar mechanical behaviours are displayed, such as the stress annihilation at some points along the boundary of elliptical voids and the stress singularity removal at the cusps/points of hypocycloidal shaped/isotoxal star-shaped polygonal voids. By means of finite element simulations it is finally shown that the presented closed-form expressions for the stress intensification provide reliable predictions even for finite domain realizations and, in particular, the infinite-plane solution remains highly accurate when the size of smooth and non-smooth external boundary is greater than twice and five times the void dimension, respectively. Under these geometrical conditions, the derived analytical expressions represent a valid 'guide tool' in mechanical design.