title: Cones of localized shear strain in incompressible elasticity with prestress: Green's function and integral representations.
abstract: The infinite-body three-dimensional Green's function set (for incremental displacement and mean stress) is derived for the incremental deformation of a uniformly strained incompressible, nonlinear elastic body. Particular cases of the developed formulation are the Mooney-Rivlin elasticity and the J2-deformation theory of plasticity. These Green's functions are used to develop a boundary integral equation framework, by introducing anad hocpotential, which paves the way for a boundary element formulation of three-dimensional problems of incremental elasticity. Results are used to investigate the behaviour of a material deformed near the limit of ellipticity and to reveal patterns of shear failure. In fact, within the investigated three-dimensional framework, localized deformations emanating from a perturbation are shown to be organized in conical geometries rather than in planar bands, so that failure is predicted to develop through curved and thin surfaces of intense shearing, as can for instance be observed in the cup-cone rupture of ductile metal bars.
authors.affiliation: Department of Civil, Environmental & Mechanical Engineering , University of Trento, via Mesiano 77 , 38123 Trento, Italy.
authors.forename: L P
authors.initials: LP
authors.lastname: Argani
authors.affiliation: Department of Civil, Environmental & Mechanical Engineering , University of Trento, via Mesiano 77 , 38123 Trento, Italy.
authors.forename: D
authors.initials: D
authors.lastname: Bigoni
authors.affiliation: Department of Architecture , University of Ferrara, Via Quartieri 8 , 44100 Ferrara, Italy.
authors.forename: D
authors.initials: D
authors.lastname: Capuani
authors.affiliation: Department of Mathematical Sciences , University of Liverpool , Liverpool L69 3BX, UK.
authors.forename: N V
authors.initials: NV
authors.lastname: Movchan
keywords: anisotropy; boundary element method; incompressible elasticity; nonlinear elasticity; prestressed material; shear bands