Effects of yield surface shape on sheet metal forming simulations

Three phenomenological yield criteria are adopted to describe the plastic behaviour of sheet metals with normal plastic anisotropy. The sheet metals are assumed to be elastic-plastic, rate-sensitive and incompressible. A rate-sensitive thin shell finite element formulation based on the virtual work principle is derived for the three yield criteria. The effects of the yield surface shapes based on the three yield criteria with the same value of the plastic anisotropy parameter R on the strain distribution and localization are investigated under a hemispherical punch stretching operation and a plane strain rawing operation. The results of the simulations show that the yield surface shape, in addition to the plastic anisotropy parameter R, controls the punch force, strain distribution and strain localization for the punch stretching operation. However, the yield surface shape does not affect the punch force and the strain distribution significantly for the plane strain drawing operation. © 1998 John Wiley & Sons, Ltd.     

Implicit constitutive modelling for viscoplasticity using neural networks

Up to now, a number of models have been proposed and discussed to describe a wide range of inelastic behaviours of materials. The fatal problem of using such models is however the existence of model errors, and the problem remains inevitably as far as a material model is written explicitly. In this paper, the authors define the implicit constitutive model and propose an implicit viscoplastic constitutive model using neural networks. In their modelling, inelastic material behaviours are generalized in a state-space representation and the state-space form is constructed by a neural network using input–output data sets. A technique to extract the input–output data from experimental data is also described. The proposed model was first generated from pseudo-experimental data created by one of the widely used constitutive models and was found to replace the model well. Then, having been tested with the actual experimental data, the proposed model resulted in a negligible amount of model errors indicating its superiority to all the existing explicit models in accuracy. © 1998 John Wiley & Sons, Ltd.     

A computational model for elasto-viscoplastic solids at finite strain with reference to thin shell applications

This work extends a previously developed methodology for computational plasticity at finite strains that is based on the exponential map and logarithmic stretches to the context of isotropic elasto-viscoplastic solids. A particular form of the strain-energy function, given in terms of its principal values is employed. It is noticeable that within the proposed framework, the small strain integration algorithms, and the corresponding consistent tangent operators, automatically extend to the finite strain regime. Central to the effort of this formulation is the derivation of the closed form of a tangent modulus obtained by linearization of incremental non-linear problem. This ensures asymptotically quadratic rates of convergence of the Newton–Raphson procedure in the implicit finite element solution. To illustrate the performance of the presented formulation, several numerical examples, involving failure by strain localization and finite deformations, are given. © 1998 John Wiley & Sons, Ltd.     

AN EFFICIENT STRESS ALGORITHM WITH APPLICATIONS IN VISCOPLASTICITY AND PLASTICITY

This paper deals with two main topics. The first one concerns the equivalence of stress algorithms, based on a Backward-Euler-step applied on viscoplastic models of Chaboche-type, and their elastoplastic counterpart. Generally, the stress algorithm yields a system of non-linear algebraic equations and the corresponding consistent tangent operator, occurring in the principle of virtual displacements, leads to a system of linear equations. This procedure can be obtained utilizing only numerical methods. The second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of Armstrong/Frederick terms, which is equivalent to a multi-surface plasticity model. Applying this model a so-called problem-adapted stress algorithm is derived, where only one non-linear equation must be solved. This result is independent of the number of terms in the hardening model. Furthermore, only the viscoplastic algorithm must be implemented, since it includes the elastoplastic constitutive model as a special case. © 1997 by John Wiley & Sons, Ltd.