Francesco Dal Corso

The interactions between shear bands and rigid lamellar inclusions in a ductile metal matrix

A ductile metal matrix (modelled as a nonlinear elastic material) containing a dilute suspension of an iso-oriented lamellar stiff phase (modelled as stiffeners, i.e. zero thickness, rigid inclusions) is subject to a simple shear of finite amount, parallel to the inclusion orientation, and subsequently perturbed through an incremental Mode I loading, uniform at infinity. Solution to this problem permits analytical investigations of the emergence of shear bands and their interaction with a rigid inclusion (involving a stress square-root singularity at its tip) and discloses the mechanisms of ductile failure in reinforced materials (explaining for instance the experimental evidence that shear bands tend to nucleate and grow parallel to thin hard inclusions). Finally, investigated beyond the elliptic range, the obtained solution becomes non-unique and reveals non-decay and singularity of the fields, facts that provide analytical justification for the difficulties associated with numerical treatment of shear bands.

A teaching model for truss structures

A classroom demonstration model has been designed, machined and successfully tested in different learning environments to facilitate understanding of the mechanics of truss structures, in which struts are subject to purely axial load and deformation. Gaining confidence with these structures is crucial for the development of lattice models, which occur in many fields of physics and engineering. (Some figures may appear in colour only in the online journal)

Strain Localization and Shear Band Propagation in Ductile Materials

A model of a shear band as a zero-thickness nonlinear interface is proposed and tested using finite element simulations. An imperfection approach is used in this model where a shear band, that is assumed to lie in a ductile matrix material (obeying von Mises plasticity with linear hardening), is present from the beginning of loading and is considered to be a zone in which yielding occurs before the rest of the matrix. This approach is contrasted with a perturbative approach, developed for a J2-deformation theory material, in which the shear band is modelled to emerge at a certain stage of a uniform deformation. Both approaches concur in showing that the shear bands (differently from cracks) propagate rectilinearly under shear loading and that a strong stress concentration should be expected to be present at the tip of the shear band, two key features in the understanding of failure mechanisms of ductile materials.