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Prof. Frédéric Barlat

GIFT, Pohang University of Science and Technology, Korea
Lecture on the constitutive modeling
for sheet metal forming


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 as 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. Finally, an introduction to anisotropic hardening theories is briefly discussed.

Prof. Toshihiko Kuwabara

Tokyo University of Agriculture and Technology, Japan
Advanced material testing methods
for high-precision sheet metal forming simulations


This lecture reviews advanced material testing methods for sheet materials: hydraulic bulge, simple shear, plane strain tension, biaxial tension using a cruciform specimen, multiaxial tube expansion, in-plane compression and cyclic tension-compression of a sheet specimen, and applications of digital image correlation method. Examples of the test results and material modeling for mild steels, high strength steels, aluminum alloys, and hcp materials are presented. In addition, the effects of the material models identified by using these testing methods on the predictive accuracy of forming simulations are discussed.