A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness - Part II: Nonlinear applications

In this work the recently proposed Reduced Enhanced Solid-Shell (RESS) finite element, based on the enhanced assumed strain (EAS) method and a one-point quadrature integration scheme, is extended in order to account for large deformation elastoplastic thin-shell problems. One of the main features of this finite element consists in its minimal number of enhancing parameters (one), sufficient to circumvent the well-known Poisson and volumetric locking phenomena, leading to a computationally efficient performance when compared to other 3D or solid-shell enhanced strain elements. Furthermore, the employed numerical integration accounts for an arbitrary number of integration points through the thickness direction within a single layer of elements. The EAS formulation comprises an additive split of the Green-Lagrange material strain tensor, making the inclusion of nonlinear kinematics a straightforward task. A corotational coordinate system is used to integrate the constitutive law and to ensure incremental objectivity. A physical stabilization procedure is implemented in order to correct the element's rank deficiencies. A variety of shell-type numerical benchmarks including plasticity, large deformations and contact are carried out, and good results are obtained when compared to well-established formulations in the literature. Copyright © 2006 John Wiley & Sons, Ltd

Modelling the plastic anisotropy of metals

peer reviewedThis work is an overview of available constitutive laws used in finite element codes to model elastoplastic metal anisotropy behaviour at a macroscopic level. It focuses on models with strong links with the phenomena occurring at microscopic level. Starting from macroscopic well-known models such as Hill or Barlat’s laws, the limits of these macroscopic phenomenological yield loci are defined, which helps to understand the current trends to develop micro-macro laws. The characteristics of micro-macro laws, where physical behaviour at the level of grains and crystals are taken into account to provide an average macroscopic answer are described. Some basic knowledge about crystal plasticity models is given for non-specialists, so every one can understand the microscopic models used to reach macroscopic values. The assumptions defining the transition between the microscopic and macroscopic scales are summarized: full constraint or relaxed Taylor’s model, self-consistent approach, homogenisation technique. Then, the two generic families of micromacro models are presented: macroscopic laws without yield locus where computations on discrete set of crystals provide the macroscopic material behaviour and macroscopic laws with macroscopic yield locus defined by microscopic computations. The models proposed by Anand, Dawson, Miehe, Geers, Kalidindi or Nakamachi belong to the first family when proposals by Montheillet, Lequeu, Darrieulat, Arminjon, Van Houtte, Habraken enter the second family. The characteristics of all these models are presented and commented. This paper enhances interests of each model and suggests possible future developments