Dynamic interaction of multiple shear bands

Abstract

A mechanical model for waves impinging different configurations of multiple shear bands already formed in a ductile material, allows to analyze the ways in which dynamic interactions promote failure. It is shown that the presence of more than one shear band may lead to resonance and correspondent growth of a shear band or, conversely, to its annihilation. At the same time, multiple scattering may bring about focusing or, conversely, shielding from waves. The proposed mechanical modelling, represents the only way to analyze the fine micromechanisms governing material collapse, and discloses the complex interplay between dynamics and shear band growth or arrest.

Interactions between multiple rigid lamellae in a ductile metal matrix: Shear band magnification and attenuation in localization patterns

“…In the limit of vanishing inclusion thickness, → 0, and considering the definition of the line domain ( ) , equation (3), of the unit normal ̂ , equation (23), and of the jump operator, equation (12), the integral equation (20) simplifies to…”

“…The collocation method is exploited to numerically solve the integral equations for the incremental equilibrium (11) and rigid-body displacement (29) of the inclusion. A special technique has to be applied to treat the stress singularity at the inclusion tips [19,20]. In particular, the mixed boundary element method [10,19,31] is implemented here with the use of discontinuous elements [9,42], necessary to overcome the difficulty connected with the singularity of the traction occurring at corner points, which correspond to the lamellae tips in our case [15,29].…”