Educational Workshop

Intensive education workshop (approximately 1.5 hours per topic) is offered for four selected areas from the world-top scientists . This is aimed in particular at the young researchers or those interested to start working in this area.

2 December, 2018
  • F. Barlat (Constitutive Modeling)
  • F. Yoshida and T. Uemori (Kinematic Hardening)
6 December, 2018
  • T.B. Stoughton (Forming Limit)
  • R. Lebensohn (Polycrystal modeling)


CONSTITUTIVE MODELING (Sunday 2 December, 14:00 – 15:30)

F. Barlat

Constitutive modeling provides relationships between stresses and strains which, in addition to the fundamental equilibrium and compatibility equations, allow the solution of boundary value problems in mechanics. In this class, these relationships are established at the continuum scale for the elasto-plastic deformations of metals. The uniaxial behavior is first reviewed because it clearly illustrates the different features observed during elasto-plasticity. Based on appropriate assumptions, the classical approaches of linear elasticity and non-linear plasticity in multiaxial loading is introduced for isotropic materials. The generalized Hooke’s law for elasticity is very briefly discussed but more emphasis is put on the flow theory of plasticity in this class. The important concepts of yield conditions, flow rules, plastic potentials and hardening laws are introduced in a clear manner. The theory is extended to the case of anisotropic materials in the most straight-forward fashion, that is, while keeping most of the concepts developed for isotropic materials, but the main differences between the isotropic and anisotropic approaches are explicitly established.

KINEMATIC HARDENING (Sunday 2 December, 16:00 – 17:30)

F. Yoshida and T. Uemori
(Hiroshima University / Okayama University, Japan)

This course will provide the framework of cyclic plasticity modeling, to describe the Bauschinger effect and cyclic workhardening of materials, based on the kinematic hardening models wherein the yield surface moves kinematically in the stress space. Various types of kinematic hardening laws, such as the linearly kinematic hardening (Prager-Drucker model), non-linear kinematic hardening laws (e.g., Armstrong-Frederick model), combined isotropic and kinematic hardening law, the multi-surface model (Mroz model), will be discussed. The Yoshida-Uemori (Y-U) model that describes the Bauschinger effect and workhardening stagnation will be specifically presented, together with the description of anisotropy evolution. A special emphasis is placed on how the use of an appropriate cyclic plasticity model is of importance for the FE simulation, especially for springback prediction, by showing several FE-simulation examples, e.g., springback after hat-shaped draw bending, S-rail forming, B-pillar forming and bumper beam forming for advanced high-strength steel sheets. A mathematical aspect for the model implementation into the FE code will be also explained.

FORMING LIMIT (Thursday 6 December, 08:30 – 10:00)

T. B. Stoughton
(General Motors Global R&D Center, USA)

This course will present basic concepts of phenomenological modelling of localized necking and fracture of metals for use in finite element simulations. The course will cover the development and application of the strain-based Forming Limit Diagram, which is favored by manufacturing engineers to draw a Forming Limit Curve that defines the boundary where onset of localized necking is expected to initiate, and the Stress Triaxiality Diagram, which is favored by product performance engineers in fracture models to define when fracture occurs during simulations of the deformation of product components. The students will learn about the methods employed to expand the utility of these diagrams to applications involving in-plane anisotropic metals and complex nonlinear loading histories, including complications introduced by out-of-plane deformation (bending/unbending), as well as the need for the unification of necking and fracture models in which, depending on the details of the history of deformation, an element of the sheet may be determined to fail by necking with or without fracture, or fracture without necking, or fracture by surface cracking without propagation of the crack through the sheet thickness.

POLYCRYSTAL MODELING (Thursday 6 December, 10:30 – 12:00)

R. Lebensohn
(Los Alamos National Laboratory, USA)

This course will present basic concepts on how to physically describe, mathematically represent, and computationally model the plastic deformation of crystalline materials. Crystal mechanics will be introduced treating each crystallite as a continuum medium, accounting for the directionality deriving from its inherent elastic anisotropy and the spatial arrangement of slip systems on which dislocations glide to accommodate plastic deformation. This mechanism-based constitutive description will be integrated using different mathematical techniques to obtain the mechanical behavior of polycrystalline aggregates made of single crystal grains, accounting for the distribution of crystal orientations (crystallographic texture), as well as the morphology and topological arrangement of the grains. In turn, these physically-based models will be applied to study the connection between microstructure and plastic anisotropy of polycrystalline aggregates, an important property of this ubiquitous class of materials in industrial applications. The students will be exposed to results of different polycrystal plasticity computational codes (VPSC, FFT-based codes) and applications of the latter to study microstructure-property relationship problems.