• Abed-Meraim, Farid

Abstract

The research work presented in this manuscript is divided into three parts. The first is concerned with the modeling of material instabilities in metallic materials (localization, necking ...). The aim is to develop theoretical and numerical tools for the prediction of these phenomena and to validate them through forming limit diagrams for ferritic and dual-phase steels. Two complementary approaches have been adopted: the first is micromechanical based on crystal plasticity coupled with appropriate scale-transition schemes, while the second is phenomenological using advanced constitutive models, which we have coupled with damage. In particular, Rice's bifurcation criterion, associated with the loss of ellipticity of the governing equations, has been investigated through these two approaches. The effect of both material or microstructure-related parameters and some destabilizing mechanisms on plastic strain localization development has been analyzed. The key role in the prediction of shear band localization of vertex formation on the current yield surface is particularly emphasized. The second part deals with structural/geometric instabilities (buckling, wrinkling ...). In this context, we proposed a new approach based on the stability analysis of the quasi-static evolution. For strain-rate sensitive materials, the absence of both bifurcation and equilibrium states motivates such a problem statement (i.e., stability of quasi-static evolutions). For elasto-plastic materials, this approach is justified by the fact that most often we are dealing with a quasi-static evolution for a given loading path, even though each point of this evolution represents an equilibrium state. The unified stability criterion that we propose requires the positiveness of the second variation of the total energy and is shown to be valid for elasto-plastic, visco-plastic or visco-elastic solids. More recently, we have extended this criterion to higher-order gradient constitutive models. Moreover, its comparison with existing results on plastic buckling allowed revisiting Hill's non-bifurcation criterion in relation to the choice of the adequate plasticity theory. The essential role played by the formation of yield surface vertices in the prediction of plastic buckling is demonstrated once again. The third part of this work deals with the development of solid-shell finite elements. The key idea of this concept is to combine the benefits of both continuum and shell elements to derive new formulations that are particularly suitable for thin-structure modeling. These enhanced formulations have the following advantages over shell elements: the avoidance of complex shell-type kinematics, the use of general three-dimensional constitutive models, direct calculation of thickness (strain) variations, easy treatment of large rotations along with simple updating of configurations, straightforward connection with 3D elements since displacements are the only degrees of freedom, and natural contact conditions on both sides of the structure. In order to improve their computational efficiency and to alleviate some membrane and shear locking phenomena, the reduced integration scheme is used. The spurious zero-energy deformation modes due to this in-plane reduced integration are efficiently controlled by an appropriate stabilization technique.

Topics

• impedance spectroscopy
• microstructure
• surface
• polymer
• phase
• theory
• steel
• forming
• plasticity
• crystal plasticity