# PICS Seminar: “A Non-local Plasticity Model for Porous Metals with Deformation-induced Anisotropy: Mathematical and Computational Issues”

## December 2 at 2:00 PM - 3:00 PM

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” λ is introduced and a “non-local” porosity is defined from the solution of a modified Helmholtz equation with appropriate boundary conditions. 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 3Rλ 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; therefore, 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.

## Nicolas Aravas

### Professor, Department of Mechanical Engineering, University of Thessaly, Volos, Greece

Nick Aravas is Professor of Computational Mechanics and Director of the Laboratory of Mechanics and Strength of Materials in the Department of Mechanical Engineering of the University of Thessaly in Greece. He has also served as the Vice-Rector for Research and Development and as Dean of Engineering at the University of Thessaly. He was born in Thessaloniki, Greece. He studied Mechanical Engineering at the Aristotelian University of Thessaloniki, Greece. He received his M.S. and Ph.D. degrees in Theoretical and Applied Mechanics from the University of Illinois at Urbana-Champaign (UIUC).

Professor Aravas started his professional career in 1985 as a Senior Engineer in Hibbitt, Karlsson and Sorensen, Inc., the developers of the ABAQUS general purpose finite element program. His academic career started in 1986 when he joined the Department of Mechanical Engineering and Applied Mechanics (MEAM) of the University of Pennsylvania (PENN), where he taught for 11 years. In 1996 he was appointed Professor of Computational Mechanics at the University of Thessaly (UTH) in Greece. While at PENN, he received the “Presidential Young Investigator Award”. He is a Fellow of ASME and has served as Associate Editor of the ASME Journal of Applied Mechanics. He received also the “Distinguished Alumni Award” from the Department of Mechanical Science and Engineering (MechSE) of the University of Illinois at Urbana-Champaign. Since 2011 Dr. Aravas is a “World Premiere International” (WPI) Professor at the International Institute for Carbon-Neutral Energy Research (I2CNER) of Kyushu University in Japan.
His interests include the areas of Plasticity, Finite Element Methods, Fracture Mechanics, and Biomechanics.

## Details

Date:
December 2
Time:
2:00 PM - 3:00 PM
Event Category:
Event Tags:
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## Organizer

Penn Institute for Computational Science (PICS)
Phone:
215-573-6037
Email:
kathom@seas.upenn.edu
View Organizer Website

## Venue

Zoom – Email MEAM for Link