dc.creator | Aravas N., Papadioti I. | en |
dc.date.accessioned | 2023-01-31T07:32:43Z | |
dc.date.available | 2023-01-31T07:32:43Z | |
dc.date.issued | 2021 | |
dc.identifier | 10.1016/j.jmps.2020.104190 | |
dc.identifier.issn | 00225096 | |
dc.identifier.uri | http://hdl.handle.net/11615/70749 | |
dc.description.abstract | A non-local (gradient) plasticity model for porous metals that accounts for deformation-induced anisotropy is presented. The model is based on the work of Ponte Castañeda and co-workers on porous materials containing randomly distributed ellipsoidal voids. It takes into account the evolution of porosity and the evolution/development of anisotropy due to changes in the shape and the orientation of the voids during plastic deformation. A “material length” ℓ is introduced and a “non-local” porosity is defined from the solution of a modified Helmholtz equation with appropriate boundary conditions, as proposed by Geers et al. (2001); Peerlings et al. (2001). At a material point located at x, the non-local porosity f(x) can be identified with the average value of the “local” porosity floc(x) over a sphere of radius R≃3ℓ centered at x. The same approach is used to formulate a non-local version of the Gurson isotropic model. The mathematical character of the resulting incremental elastoplastic partial differential equations of the non-local model is analyzed. It is shown that the hardening modulus of the non-local model is always larger than the corresponding hardening modulus of the local model; as a consequence, the non-local incremental problem retains its elliptic character and the possibility of discontinuous solutions is eliminated. A rate-dependent version of the non-local model is also developed. An algorithm for the numerical integration of the non-local constitutive equations is developed, and the numerical implementation of the boundary value problem in a finite element environment is discussed. An analytical method for the required calculation of the eigenvectors of symmetric second-order tensors is presented. The non-local model is implemented in ABAQUS via a material “user subroutine” (UMAT or VUMAT) and the coupled thermo-mechanical solution procedure, in which temperature is identified with the non-local porosity. Several example problems are solved numerically and the effects of the non-local formulation on the solution are discussed. In particular, the problems of plastic flow localization in plane strain tension, the plane strain mode-I blunt crack tip under small-scale-yielding conditions, the cup-and-cone fracture of a round bar, and the Charpy V-notch test specimen are analyzed. © 2020 Elsevier Ltd | en |
dc.language.iso | en | en |
dc.source | Journal of the Mechanics and Physics of Solids | en |
dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85092708934&doi=10.1016%2fj.jmps.2020.104190&partnerID=40&md5=52f1fc6b9efc897fa23fc3fc1c25d405 | |
dc.subject | Anisotropy | en |
dc.subject | Boundary conditions | en |
dc.subject | Boundary value problems | en |
dc.subject | Constitutive equations | en |
dc.subject | Crack tips | en |
dc.subject | Hardening | en |
dc.subject | Numerical methods | en |
dc.subject | Porous materials | en |
dc.subject | Strain | en |
dc.subject | Coupled thermo-mechanical | en |
dc.subject | Deformation induced anisotropy | en |
dc.subject | Discontinuous solutions | en |
dc.subject | Modified helmholtz equations | en |
dc.subject | Numerical implementation | en |
dc.subject | Numerical integrations | en |
dc.subject | Plastic flow localization | en |
dc.subject | Second-order tensors | en |
dc.subject | Porosity | en |
dc.subject | Elsevier Ltd | en |
dc.title | A non-local plasticity model for porous metals with deformation-induced anisotropy: Mathematical and computational issues | en |
dc.type | journalArticle | en |