Stress concentration near stiff inclusions: validation of rigid inclusion model and boundary layers by means of photoelasticity

TL;DR

This study uses photoelasticity to experimentally validate the stress concentration predictions of the rigid inclusion model near stiff inclusions in elastic plates, highlighting boundary layer effects and shape dependence.

Contribution

It provides experimental validation of the rigid inclusion model and boundary layer effects, advancing understanding of stress fields around stiff inclusions in elastic materials.

Findings

Singularity is lower for obtuse than for acute inclusion angles.

Stronger singularity observed in Mode II than Mode I.

Validation of the rigid quadrilateral inclusion model.

Abstract

Photoelasticity is employed to investigate the stress state near stiff rectangular and rhombohedral inclusions embedded in a 'soft' elastic plate. Results show that the singular stress field predicted by the linear elastic solution for the rigid inclusion model can be generated in reality, with great accuracy, within a material. In particular, experiments: (i.) agree with the fact that the singularity is lower for obtuse than for acute inclusion angles; (ii.) show that the singularity is stronger in Mode II than in Mode I (differently from a notch); (iii.) validate the model of rigid quadrilateral inclusion; (iv.) for thin inclusions, show the presence of boundary layers deeply influencing the stress field, so that the limit case of rigid line inclusion is obtained in strong dependence on the inclusion's shape. The introduced experimental methodology opens the possibility of enhancing the design of thin reinforcements and of analyzing complex situations involving interaction between inclusions and defects.