An inverse method for material parameters estimation in the inelastic range

Abstract

Inverse problem theory is getting of an increasing importance in mechanical modelling as it brings a solution to the identification to rheological behaviour of materials in the nonlinear range. As a matter of fact, when using inverse identification, the problem of experimental tests interpretation associated to inhomogeneous deformation states is bypassed. This allows a more accurate material parameters determination compared to the direct identification. In this paper, an inverse identification method is proposed to determine material parameters in the nonlinear range. The algorithm developed consists of a finite element based inversion scheme associated to an optimization procedure. A sensitivity analysis is used in order to determine the gradient of the cost function, representing the difference between the measured and the calculated response, with respect to the material parameters to identify. This method is applied to the inverse identification of viscoplastic parameters entering in the constitutive function that describes the flow stress of an aluminium alloy, for large range of strain, strain rate and temperature.