  A shear band of finite length, formed inside a ductile material at a certain
stage of a con- tinued homogeneous strain, provides a dynamic perturbation to
an incident wave field, which strongly influences the dynamics of the material
and affects its path to failure. The investigation of this perturbation is
presented for a ductile metal, with reference to the incremental mechanics of a
material obeying the J 2-deformation theory of plasticity (a special form of
prestressed, elastic, anisotropic, and incompressible solid). The treatment
originates from the derivation of integral representations relating the
incremental mechan- ical fields at every point of the medium to the incremental
displacement jump across the shear band faces, generated by an impinging wave.
The boundary integral equations (under the plane strain assumption) are
numerically approached through a collocation technique, which keeps into
account the singularity at the shear band tips and permits the analysis of an
incident wave impinging a shear band. It is shown that the presence of the
shear band induces a resonance, visible in the incremental displacement field
and in the stress intensity factor at the shear band tips, which promotes shear
band growth. Moreover, the waves scattered by the shear band are shown to
generate a fine texture of vibrations, par- allel to the shear band line and
propagating at a long distance from it, but leaving a sort of conical shadow
zone, which emanates from the tips of the shear band.
