A rigid line inclusion, also called stiffener, is a mathematical model used in solid mechanics to describe a narrow hard phase, dispersed within a matrix material. This inclusion is idealised as an infinitely rigid and thin reinforcement, so that it represents a sort of ‘inverse’ crack, from which the nomenclature ‘anticrack’ derives.

From the mechanical point of view, a stiffener introduces a kinematical constraint, imposing that it may only suffer a rigid body motion along its line.

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

Photoelasticity

Photoelasticity is an experimental method to determine the stress distribution in a material. The method is mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress...

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Shear bands emerging at the stiffener tip

Analytical solutions obtained in prestressed elasticity show the possibility of the emergence of shear band

Shear band

A shear band is a narrow zone of intense shearing strain, usually of plastic nature, developing during severe deformation of ductile materials....

s at the tip of the stiffener .

External links

• Laboratory for Physical Modeling of Structures and Photoelasticity (University of Trento, Italy)