Rigid line inclusion

Theoretical model

The stiffener model has been used to investigate different mechanical problems in classical elasticity (load diffusion, inclusion at bi material interface ).

The main characteristics of the theoretical solutions are basically the following.

1. Similarly to a fracture, a square-root singularity in the stress/strain fields is present at the tip of the inclusion.
2. 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.

Experimental validation

The characteristics of the elastic solution have been experimentally confirmed through photoelastic transmission experiments.

Interaction of rigid line inclusions

The interaction of rigid line inclusions in parallel, collinear and radial configurations have been studied using the boundary element method (BEM) and validated using photoelasticity.

Shear bands emerging at the stiffener tip

Analytical solutions obtained in prestressed elasticity show the possibility of the emergence of shear bands at the tip of the stiffener.

References

References

1. Koiter, W.T., On the diffusion of load from a stiffener into a sheet. Q. J. Mech. Appl. Math. 1955, VIII, 164–178.
2. Ballarini, R., A rigid line inclusion at a bimaterial interface. Eng. Fract. Mech., 1990, 37, 1–5.
3. (2010). "The stress intensity near a stiffener disclosed by photoelasticity". International Journal of Fracture.
4. (2019). "Numerical evaluation of the interaction of rigid line inclusions using strain intensity factors". International Journal of Mechanical Sciences.
5. Bigoni, D. Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability. Cambridge University Press, 2012 . {{ISBN. 9781107025417.
6. (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.
7. (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.
8. (2008). "The interactions between shear bands and rigid lamellar inclusions in a ductile metal matrix". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.