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 an ad hoc potential, 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.
Scheda prodotto non validato
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo
|Titolo:||Cones of localized shear strain in incompressible elasticity with prestress: Green's function and integral representations|
|Autori interni:||CAPUANI, Domenico|
|Data di pubblicazione:||2014|
|Rivista:||PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A|
|Appare nelle tipologie:|