Identification of Orthotropic Material Behaviour Using the Error in Constitutive Equation

Abstract

The aim of this work is to allow the simultaneous identification of the mechanical parameter governing an orthotropic behaviour law from one single specimen. The chosen mechanical test is a non-standard geometry used in a latest works Meuwissen et al. [1] as shown in Fig. 1. It was shown that this test is appropriate for giving rise to heterogeneous stress/strain fields from which the whole set of material parameters are involved. The identification procedure consists in a processing of the strain fields and minimising a cost function constructed form a fundamental variational principle, namely the error in constitutive equation proposed by Bonnet et al. [2]. The inverse problem is optimised using the regularised Levenberg-Marquardt algorithm. To illustrate the pertinence and the numerical stability of the procedure, the identification is performed on data provided by finite element simulations ABAQUS [3]. In this work, numerical aspects inherent to the identification procedure sensitivity in terms of accuracy and stability were investigated. A systematic error due to a shift image and white Gaussian noise (random) were added to strain values provided by FE computations to simulate an experimental errors. Only the last one is presented in this abstract. Several identifications with different guess values of the parameters are performed. Identified values are reported in table 1. For each case of the initial values, all behaviour parameters (Qij) were identified with a high accuracy and stability even from noisy strain fields. The experimental implementation of the method is currently on-going and will be presented in the final paper.