Rigid line inclusion
Mathematical model used in solid mechanics
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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,[1] inclusion at bi material interface [2]).
The main characteristics of the theoretical solutions are basically the following.
- 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.
Experimental validation
The characteristics of the elastic solution have been experimentally confirmed through photoelastic transmission experiments.[3]
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.[4]
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.[5][6][7][8]