# Thin inclusion reinforcement (stiffener)

# Summary

The presence of a second phase in a matrix material leads to inhomogeneity in the mechanical fields. The theoretical solution of a zero-thickness, infinitely rigid line inclusion embedded in an elastic material has the following features:

- similarly to a fracture, a square-root singularity in the stress/strain fields is present at the tip of the inclusion;
- in a homogeneous matrix subject to uniform stress at infinity, such singularity only arises when a normal stress acts parallel or orthogonal to the inclusion line, while a stiffener parallel to a simple shear does not disturb the ambient field.

We have confirmed these characteristics through photoelastic transmission experiments.

# Related papers:

- Noselli, G., Dal Corso, F. and Bigoni, D. (2010).

The stress intensity near a stiffener disclosed by photoelasticity.*International Journal of Fracture*,**166**(1-2), 91-103. - Dal Corso, F. and Bigoni, D. (2009).

The interactions between shear bands and rigid lamellar inclusions in a ductile metal matrix.*Proceedings of the Royal Society A*,**465**(2101), 143-163. - Dal Corso, F., Bigoni, D. and Gei, M. (2008).

The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part I. Full field solution and asymptotics.*Journal of the Mechanics and Physics of Solids*,**56**(3), 815-838. - Bigoni, D., Dal Corso, F. and Gei, M. (2008).

The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part II. Implications on shear band nucleation, growth and energy release rate.*Journal of the Mechanics and Physics of Solids*,**56**(3), 839-857.