The unrestrainable growth of a shear band in a prestressed material

Abstract

A weak line inclusion model in a nonlinear elastic solid is proposed to analytically quantify and investigate, for the first time, the stress state and growth conditions of a finite-length shear band in a ductile prestressed metallic material. The deformation is shown to become highly focused and aligned coaxial to the shear band-a finding that provides justification for the experimentally observed strong tendency towards rectilinear propagation-and the energy release rate to blow up to infinity, for incremental loading occurring when the prestress approaches the elliptic boundary. It is concluded that the propagation becomes 'unrestrainable', a result substantiating the experimental observation that shear bands are the preferential near-failure deformation modes.

Integral Identities for a Semi-infinite Interfacial Crack in 2D and 3D Elasticity

“…Purely numerical methods, such as finite element and boundary element techniques, are very popular and extensively used, thanks to the computational power of modern computers. However, analytical methods, such as integral transforms, variational inequalities, and singular integral equations, are still of great interest, for instance in deriving fundamental solutions for some basic geometries (to be employed in numerical methods), in the assertion of existence and uniqueness of the solution, and in bifurcation theory (Bigoni and Capuani, 2002;Bigoni and Dal Corso, 2008).…”

Complex Dynamical Behavior in the Shear‐Displacement Model for Bulk Metallic Glasses during Plastic Deformation

“…= / (1 + ), where is the Young modulus of the metallic glass and is the stiffness ratio of sample to the testing machine = / = 2 /(4 ) [19]. The propagation of the shear bands can be considered as a wave propagating in homogeneous isotropic elastic body [20,21]. To solve the partial differential equation 2, the strain evolution was traced during the deformation by analyzing the traveling wave transformation, = − , where is the speed of the traveling wave, ( , ) = ( ).…”

The role of electrostriction on the stability of dielectric elastomer actuators

“…• to analyze band-localization instability in homogeneous DEs, in particular facing its relation with the constitutive properties of the solid. The theory developed here extends to the electroelastic domain the well-known theory of localization of deformation in nonlinear elasticity, where the existence of a localized solution of the incremental problem -concentrated within a narrow band -is sought along the loading path (Rice, 1973;Hill and Hutchinson, 1975;Bigoni and Dal Corso, 2008).…”