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

A ductile matrix material containing an arbitrary distribution of parallel and stiff lamellar (’rigid-line’) inclusions is considered, subject to a prestress state provided by simple shear aligned the inclusion lines. Because lamellae have negligible thickness, remains uniform its amount can be high enough drive on verge ellipticity loss. Close this critical stage, remote Mode I perturbation realizes band formation, growth, interaction, thickening or thinning. This two-dimensional problem solved through derivation specific boundary integral equations, holding for nonlinear elastic uniformly prestressed; related numerical treatment specifically tailored capture stress singularity present at tips. Results show how complex localized deformation patterns form, so explaining features failure mechanisms materials reinforced with thin inclusions. In particular, influence bands pattern disclosed. Conditions magnification (the attenuation) deformations are revealed, fostering progress setback) process.