Identification of plastic constitutive parameters at large deformations from three dimensional displacement fields

Abstract

The aim of this paper is to provide a general procedure to extract the constitutive parameters of a plasticity model starting from displacement measurements and using the Virtual Fields Method. This is a classical inverse problem which has been already investigated in the literature, however several new features are developed here. First of all the procedure applies to a general three-dimensional displacement field which leads to large plastic deformations, no assumptions are made such as plane stress or plane strain although only pressure-independent plasticity is considered. Moreover the equilibrium equation is written in terms of the deviatoric stress tensor that can be directly computed from the strain field without iterations. Thanks to this, the identification routine is much faster compared to other inverse methods such as finite element updating. The proposed method can be a valid tool to study complex phenomena which involve severe plastic deformation and where the state of stress is completely triaxial, e.g. strain localization or necking occurrence. The procedure has been validated using a three dimensional displacement field obtained from a simulated experiment. The main potentialities as well as a first sensitivity study on the influence of measurement errors are illustrated.

Application of the virtual fields method to large strain anisotropic plasticity

“…In the present case, the smoothing was performed using 7 points (m = 3). Error -0.24% -47.68% -1.59% 1.09% -2.73% 1.73% Table 2: Influence of noise on VFM identification the hardening law (Rossi and Pierron, 2012a). Therefore its variation does not introduce significant modification in the identified true stress-true strain curve.…”

“…In this paper, the procedure described by Rossi and Pierron (2012a) has been used, adapted to the plane stress condition and the Hill48 yield criterion. The idea is that the stress field at time t can be derived directly from the direction of the plastic flow and the cumulated equivalent plastic strain.…”

“…The procedure above, applied to the Hill48 yield function, is general and can be adapted to any plasticity model with a convex yield locus. For more in-depth insight on this, the reader is referred to Rossi and Pierron (2012a).…”

“…The first application of VFM to anisotropic plasticity was published by Rossi and Pierron (2012a), where a complete three-dimensional framework for large strain plasticity is presented, an application to planar anisotropy was then developed by Kim et al (2014) using Σ-shaped specimens.…”

Tribological behaviour and local mechanical properties of magnesium-alumina composites

“…where ε eq pl is the equivalent accumulated plastic strain, and K, ε 0 , n are the parameters to be identified by Camfit [15][16][17]. Figure 13 shows stress fields σ x , σ y , τ xy (MPa) obtained by the Matlab program for 25 % strain (Fig.…”